Add <math><mstyle displaystyle="true"><mn>72</mn><mi>x</mi></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>83</mn></mstyle></math> to both sides of the equation.

Use the quadratic formula to find the solutions.

Substitute the values <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>16</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>72</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi><mo>=</mo><mn>83</mn></mstyle></math> into the quadratic formula and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>64</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>83</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>5312</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>5184</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>128</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>128</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>128</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>128</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>128</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>8</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>128</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>8</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

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

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>72</mn><mo>±</mo><mn>8</mn><mi>i</mi><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>32</mn></mrow></mfrac></mstyle></math> .

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