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

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

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>19</mn><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 <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>8</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>8</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>8</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math> .

Expand <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>8</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"><mn>8</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>8</mn><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>8</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"><mn>16</mn><mi>x</mi></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>19</mn></mstyle></math> to the left side of the equation by subtracting it from both sides.

Subtract <math><mstyle displaystyle="true"><mn>19</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>14</mn><mi>x</mi><mo>+</mo><mn>45</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>45</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mn>14</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 the first factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve.

Set the first factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> from both sides of the equation.

Set the next factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve.

Set the next factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> from 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>5</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>9</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><mo>+</mo><mn>19</mn></msqrt><mo>-</mo><mn>8</mn><mo>=</mo><mi>x</mi></mstyle></math> true.

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