Solve Using the Quadratic Formula 100x^2-49=0

$100 x^{2} - 49 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 100$ , $b = 0$ , and $c = - 49$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (100 \cdot - 49)}}{2 \cdot 100}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 100 \cdot - 49}}{2 \cdot 100}$

Multiply $- 4 \cdot 100 \cdot - 49$ .

Multiply $- 4$ by $100$ .

$x = \frac{0 \pm \sqrt{0 - 400 \cdot - 49}}{2 \cdot 100}$

Multiply $- 400$ by $- 49$ .

$x = \frac{0 \pm \sqrt{0 + 19600}}{2 \cdot 100}$

Add $0$ and $19600$ .

$x = \frac{0 \pm \sqrt{19600}}{2 \cdot 100}$

Rewrite $19600$ as $140^{2}$ .

$x = \frac{0 \pm \sqrt{140^{2}}}{2 \cdot 100}$

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

$x = \frac{0 \pm 140}{2 \cdot 100}$

Multiply $2$ by $100$ .

$x = \frac{0 \pm 140}{200}$

Simplify $\frac{0 \pm 140}{200}$ .

$x = \frac{\pm 7}{10}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{7}{10}, - \frac{7}{10}$