Add <math><mstyle displaystyle="true"><mn>4</mn><mi>a</mi><mi>c</mi></mstyle></math> to both sides of the inequality.

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

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

Simplify the right side of the equation.

Rewrite <math><mstyle displaystyle="true"><mn>4</mn><mi>a</mi><mi>c</mi></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>a</mi><mi>c</mi><mo>)</mo></mrow></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> .

Add parentheses.

Pull terms out from under the radical.

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

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. Since this is an inequality, flip the direction of the inequality sign on the <math><mstyle displaystyle="true"><mo>-</mo></mstyle></math> portion of the solution.

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

Simplify <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>4</mn><mo>⋅</mo><mrow><mo>(</mo><mn>1</mn><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Simplify each term.

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

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

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> from both sides of the inequality.

Divide each term by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>a</mi><mo>></mo><mo>-</mo><mn>16</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Find the intersection of <math><mstyle displaystyle="true"><mi>D</mi><mo>></mo><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>></mo><mn>2</mn><msqrt><mi>a</mi><mi>c</mi></msqrt><mo> or </mo><mi>b</mi><mo><</mo><mo>-</mo><mn>2</mn><msqrt><mi>a</mi><mi>c</mi></msqrt></mstyle></math> .

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