Algebra Examples

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

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $32$ from both sides of the equation.

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

Step 1.2

Add $50 x^{2}$ to both sides of the equation.

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

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 50$ , $b = 0$ , and $c = - 32$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (50 \cdot - 32)}}{2 \cdot 50}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 50 \cdot - 32}}{2 \cdot 50}$

Step 4.1.2

Multiply $- 4 \cdot 50 \cdot - 32$ .

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Step 4.1.2.1

Multiply $- 4$ by $50$ .

$x = \frac{0 \pm \sqrt{0 - 200 \cdot - 32}}{2 \cdot 50}$

Step 4.1.2.2

Multiply $- 200$ by $- 32$ .

$x = \frac{0 \pm \sqrt{0 + 6400}}{2 \cdot 50}$

Step 4.1.3

Add $0$ and $6400$ .

$x = \frac{0 \pm \sqrt{6400}}{2 \cdot 50}$

Step 4.1.4

Rewrite $6400$ as $80^{2}$ .

$x = \frac{0 \pm \sqrt{80^{2}}}{2 \cdot 50}$

Step 4.1.5

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

$x = \frac{0 \pm 80}{2 \cdot 50}$

Step 4.2

Multiply $2$ by $50$ .

$x = \frac{0 \pm 80}{100}$

Step 4.3

Simplify $\frac{0 \pm 80}{100}$ .

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

Step 5

The final answer is the combination of both solutions.

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