Solve for x square root of 2x^2-7=5

$\sqrt{2 x^{2} - 7} = 5$

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

${\sqrt{2 x^{2} - 7}}^{2} = 5^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x^{2} - 7}$ as ${(2 x^{2} - 7)}^{\frac{1}{2}}$ .

${({(2 x^{2} - 7)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(2 x^{2} - 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x^{2} - 7)}^{\frac{1}{2}})}^{2}$ .

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

${(2 x^{2} - 7)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x^{2} - 7)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(2 x^{2} - 7)}^{1} = 5^{2}$

Simplify.

$2 x^{2} - 7 = 5^{2}$

Simplify the right side.

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

$2 x^{2} - 7 = 25$

Solve for $x$ .

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

Add $7$ to both sides of the equation.

$2 x^{2} = 25 + 7$

Add $25$ and $7$ .

$2 x^{2} = 32$

Divide each term in $2 x^{2} = 32$ by $2$ and simplify.

Divide each term in $2 x^{2} = 32$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{32}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{32}{2}$

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

$x^{2} = \frac{32}{2}$

Simplify the right side.

Divide $32$ by $2$ .

$x^{2} = 16$

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

$x = \pm \sqrt{16}$

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

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

$x = \pm 4$

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.

$x = 4$

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

$x = - 4$

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

$x = 4, - 4$

Solve for x square root of 2x^2-7=5

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