Solve for x square root of 9x^2-11=5

$\sqrt{9 x^{2} - 11} = 5$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{9 x^{2} - 11}}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 x^{2} - 11}$ as ${(9 x^{2} - 11)}^{\frac{1}{2}}$ .

${({(9 x^{2} - 11)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(9 x^{2} - 11)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(9 x^{2} - 11)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(9 x^{2} - 11)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(9 x^{2} - 11)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(9 x^{2} - 11)}^{1} = 5^{2}$

Simplify.

$9 x^{2} - 11 = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$9 x^{2} - 11 = 25$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $11$ to both sides of the equation.

$9 x^{2} = 25 + 11$

Add $25$ and $11$ .

$9 x^{2} = 36$

Divide each term in $9 x^{2} = 36$ by $9$ and simplify.

Divide each term in $9 x^{2} = 36$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{36}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{36}{9}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{36}{9}$

Simplify the right side.

Divide $36$ by $9$ .

$x^{2} = 4$

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

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

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

First, use the positive value of the $\pm$ to find the first solution.

$x = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2$

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

$x = 2, - 2$

Solve for x square root of 9x^2-11=5

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