Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Multiply each term in <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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.

Simplify each term.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Simplify <math><mstyle displaystyle="true"><mn>12</mn><mo>+</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Simplify each term.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

To write <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Factor the perfect trinomial square into <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><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><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></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"><msqrt><mfrac><mrow><mn>57</mn></mrow><mrow><mn>4</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>57</mn></msqrt></mrow><mrow><msqrt><mn>4</mn></msqrt></mrow></mfrac></mstyle></math> .

Simplify the denominator.

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, assuming positive real numbers.

Remove parentheses.

Subtract <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> from both sides of the equation.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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