Solve for x 4 = square root of 25-x^2

$4 = \sqrt{25 - x^{2}}$

Rewrite the equation as $\sqrt{25 - x^{2}} = 4$ .

$\sqrt{25 - x^{2}} = 4$

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

${\sqrt{25 - x^{2}}}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{25 - x^{2}}$ as ${(25 - x^{2})}^{\frac{1}{2}}$ .

${({(25 - x^{2})}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${({(25 - x^{2})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(25 - x^{2})}^{\frac{1}{2}})}^{2}$ .

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

${(25 - x^{2})}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(25 - x^{2})}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(25 - x^{2})}^{1} = 4^{2}$

Simplify.

$25 - x^{2} = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$25 - x^{2} = 16$

Solve for $x$ .

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

Subtract $25$ from both sides of the equation.

$- x^{2} = 16 - 25$

Subtract $25$ from $16$ .

$- x^{2} = - 9$

Divide each term in $- x^{2} = - 9$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 9$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 9}{- 1}$

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

$x^{2} = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$x^{2} = 9$

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.

$x = 3, - 3$

Solve for x 4 = square root of 25-x^2

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