Find All Complex Solutions 16x^2=100

$16 x^{2} = 100$

Step 1

Subtract $100$ from both sides of the equation.

$16 x^{2} - 100 = 0$

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 $a = 16$ , $b = 0$ , and $c = - 100$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (16 \cdot - 100)}}{2 \cdot 16}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 16 \cdot - 100}}{2 \cdot 16}$

Multiply $- 4 \cdot 16 \cdot - 100$ .

Multiply $- 4$ by $16$ .

$x = \frac{0 \pm \sqrt{0 - 64 \cdot - 100}}{2 \cdot 16}$

Multiply $- 64$ by $- 100$ .

$x = \frac{0 \pm \sqrt{0 + 6400}}{2 \cdot 16}$

Add $0$ and $6400$ .

$x = \frac{0 \pm \sqrt{6400}}{2 \cdot 16}$

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

$x = \frac{0 \pm \sqrt{80^{2}}}{2 \cdot 16}$

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

$x = \frac{0 \pm 80}{2 \cdot 16}$

Multiply $2$ by $16$ .

$x = \frac{0 \pm 80}{32}$

Simplify $\frac{0 \pm 80}{32}$ .

$x = \frac{\pm 5}{2}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{2}, - \frac{5}{2}$