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:

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