Subtract <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

To remove the radical on the left side of the equation, square both sides of the equation.

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>2</mn><mi>x</mi></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify.

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>)</mo></mrow></mstyle></math> .

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>)</mo></mrow></mstyle></math> using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Move <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>x</mi></mstyle></math> .

Since <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> is on the right side of the equation, switch the sides so it is on the left side of the equation.

Move all terms containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the left side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>10</mn><mi>x</mi><mo>+</mo><mn>16</mn></mstyle></math> using the AC method.

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mo>-</mo><mn>10</mn></mstyle></math> .

Write the factored form using these integers.

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>8</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>8</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> to both sides of the equation.

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>2</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>2</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to both sides of the equation.

The final solution is all the values that make <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>8</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Exclude the solutions that do not make <math><mstyle displaystyle="true"><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>+</mo><mn>7</mn><mo>=</mo><mi>x</mi><mo>+</mo><mn>3</mn></mstyle></math> true.

Do you know how to Solve the Rational Equation for x square root of 2x+7=x+3? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | four hundred twelve million eight hundred forty thousand six hundred seventy-eight |
---|

- 412840678 has 16 divisors, whose sum is
**638668800** - The reverse of 412840678 is
**876048214** - Previous prime number is
**43**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 40
- Digital Root 4

Name | one billion one hundred seventy-seven million ten thousand one hundred eighty-seven |
---|

- 1177010187 has 16 divisors, whose sum is
**1585723392** - The reverse of 1177010187 is
**7810107711** - Previous prime number is
**197**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 33
- Digital Root 6

Name | one billion four hundred fifty-one million eight hundred sixty-five thousand seventy-five |
---|

- 1451865075 has 8 divisors, whose sum is
**2013253008** - The reverse of 1451865075 is
**5705681541** - Previous prime number is
**25**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 42
- Digital Root 6