Solve Using the Quadratic Formula x^2+7x=0

$x^{2} + 7 x = 0$

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 $a = 1$ , $b = 7$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 0$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 0}}{2 \cdot 1}$

Multiply $- 4$ by $0$ .

$x = \frac{- 7 \pm \sqrt{49 + 0}}{2 \cdot 1}$

Add $49$ and $0$ .

$x = \frac{- 7 \pm \sqrt{49}}{2 \cdot 1}$

Rewrite $49$ as $7^{2}$ .

$x = \frac{- 7 \pm \sqrt{7^{2}}}{2 \cdot 1}$

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

$x = \frac{- 7 \pm 7}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm 7}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 0, - 7$