To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

Add the term to each side of the equation.

Raise <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mn>31</mn><mo>+</mo><msup><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>31</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>121</mn></mstyle></math> .

Factor the perfect trinomial square into <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>11</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Take the square root of each side of the equation to set up the solution for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math>

Remove the perfect root factor <math><mstyle displaystyle="true"><mi>x</mi><mo>+</mo><mn>11</mn></mstyle></math> under the radical to solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Simplify the right side of the equation.

Rewrite <math><mstyle displaystyle="true"><mn>152</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>38</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>152</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Remove parentheses.

Subtract <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> from both sides of the equation.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you know how to Solve by Completing the Square x^2+22x=31? 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 | one hundred fifty-three million one hundred sixty-eight thousand seven hundred fifty-seven |
---|

- 153168757 has 8 divisors, whose sum is
**200057216** - The reverse of 153168757 is
**757861351** - Previous prime number is
**7**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 43
- Digital Root 7

Name | ninety-seven million six hundred thirty-eight thousand seven hundred seventy-seven |
---|

- 97638777 has 8 divisors, whose sum is
**104048160** - The reverse of 97638777 is
**77783679** - Previous prime number is
**19**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 54
- Digital Root 9

Name | six hundred twenty-seven million seven hundred seventy-one thousand one hundred ninety-nine |
---|

- 627771199 has 4 divisors, whose sum is
**684841320** - The reverse of 627771199 is
**991177726** - Previous prime number is
**11**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 49
- Digital Root 4