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

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{2} - 5}$ as ${(x^{2} - 5)}^{\frac{1}{2}}$ .

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

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

Subtract $7$ from both sides of the equation.

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

Subtract $7$ from $5$ .

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

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Simplify the exponent.

Simplify the left side.

Simplify ${({(x^{2} - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x^{2} - 5)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$x^{2} - 5 = 4$

Solve for $x$ .

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

Add $5$ to both sides of the equation.

$x^{2} = 4 + 5$

Add $4$ and $5$ .

$x^{2} = 9$

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

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

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

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

Exclude the solutions that do not make $\sqrt{x^{2} - 5} + 7 = 5$ true.

$No solution$

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

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