Solve Using the Quadratic Formula 5x^2+9=14

$5 x^{2} + 9 = 14$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $14$ from both sides of the equation.

$5 x^{2} + 9 - 14 = 0$

Subtract $14$ from $9$ .

$5 x^{2} - 5 = 0$

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 $a = 5$ , $b = 0$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (5 \cdot - 5)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 5 \cdot - 5}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 5$ .

Multiply $- 4$ by $5$ .

$x = \frac{0 \pm \sqrt{0 - 20 \cdot - 5}}{2 \cdot 5}$

Multiply $- 20$ by $- 5$ .

$x = \frac{0 \pm \sqrt{0 + 100}}{2 \cdot 5}$

Add $0$ and $100$ .

$x = \frac{0 \pm \sqrt{100}}{2 \cdot 5}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{0 \pm \sqrt{10^{2}}}{2 \cdot 5}$

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

$x = \frac{0 \pm 10}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{0 \pm 10}{10}$

Simplify $\frac{0 \pm 10}{10}$ .

$x = \pm 1$

Step 5

The final answer is the combination of both solutions.

$x = 1, - 1$