Solve Using the Quadratic Formula 5x^2=45

$5 x^{2} = 45$

Step 1

Subtract $45$ from both sides of the equation.

$5 x^{2} - 45 = 0$

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 $c = - 45$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (5 \cdot - 45)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 5 \cdot - 45}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 45$ .

Multiply $- 4$ by $5$ .

$x = \frac{0 \pm \sqrt{0 - 20 \cdot - 45}}{2 \cdot 5}$

Multiply $- 20$ by $- 45$ .

$x = \frac{0 \pm \sqrt{0 + 900}}{2 \cdot 5}$

Add $0$ and $900$ .

$x = \frac{0 \pm \sqrt{900}}{2 \cdot 5}$

Rewrite $900$ as $30^{2}$ .

$x = \frac{0 \pm \sqrt{30^{2}}}{2 \cdot 5}$

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

$x = \frac{0 \pm 30}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{0 \pm 30}{10}$

Simplify $\frac{0 \pm 30}{10}$ .

$x = \pm 3$

Step 5

The final answer is the combination of both solutions.

$x = 3, - 3$