Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math> .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

To write <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>16</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>16</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn><mo>⋅</mo><mn>16</mn><mo>-</mo><mn>9</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math> in a factored form.

Factor <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>9</mn><mo>⋅</mo><mn>16</mn><mo>-</mo><mn>9</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>9</mn><mo>⋅</mo><mn>16</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>9</mn><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow><mo>+</mo><mn>9</mn><mrow><mo>(</mo><mo>-</mo><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Since both terms are perfect squares, factor using the difference of squares formula, <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> where <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>3</mn></mstyle></math> .

Simplify.

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>+</mo><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Factor the perfect power <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mn>9</mn><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Factor the perfect power <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Rearrange the fraction <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>+</mo><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>1</mn></mrow></mfrac></mstyle></math> .

Pull terms out from under the radical.

One to any power is one.

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><msqrt><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msqrt></mstyle></math> .

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

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