Solve for x 0=32-50x^2

$0 = 32 - 50 x^{2}$

Rewrite the equation as $32 - 50 x^{2} = 0$ .

$32 - 50 x^{2} = 0$

Subtract $32$ from both sides of the equation.

$- 50 x^{2} = - 32$

Divide each term in $- 50 x^{2} = - 32$ by $- 50$ and simplify.

Divide each term in $- 50 x^{2} = - 32$ by $- 50$ .

$\frac{- 50 x^{2}}{- 50} = \frac{- 32}{- 50}$

Simplify the left side.

Cancel the common factor of $- 50$ .

Cancel the common factor.

$\frac{- 50 x^{2}}{- 50} = \frac{- 32}{- 50}$

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

$x^{2} = \frac{- 32}{- 50}$

Simplify the right side.

Cancel the common factor of $- 32$ and $- 50$ .

Factor $- 2$ out of $- 32$ .

$x^{2} = \frac{- 2 (16)}{- 50}$

Cancel the common factors.

Factor $- 2$ out of $- 50$ .

$x^{2} = \frac{- 2 \cdot 16}{- 2 \cdot 25}$

Cancel the common factor.

$x^{2} = \frac{- 2 \cdot 16}{- 2 \cdot 25}$

Rewrite the expression.

$x^{2} = \frac{16}{25}$

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

$x = \pm \sqrt{\frac{16}{25}}$

Simplify $\pm \sqrt{\frac{16}{25}}$ .

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{25}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{25}}$

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

$x = \pm \frac{4}{\sqrt{25}}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{4}{\sqrt{5^{2}}}$

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

$x = \pm \frac{4}{5}$

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.

$x = \frac{4}{5}$

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

$x = - \frac{4}{5}$

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

$x = \frac{4}{5}, - \frac{4}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}, - \frac{4}{5}$

Decimal Form:

$x = 0.8, - 0.8$

Solve for x 0=32-50x^2

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