Solve Using the Quadratic Formula x^2+4x=15

$x^{2} + 4 x = 15$

Step 1

Subtract $15$ from both sides of the equation.

$x^{2} + 4 x - 15 = 0$

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 $a = 1$ , $b = 4$ , and $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (1 \cdot - 15)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 15}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 15$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 15}}{2 \cdot 1}$

Multiply $- 4$ by $- 15$ .

$x = \frac{- 4 \pm \sqrt{16 + 60}}{2 \cdot 1}$

Add $16$ and $60$ .

$x = \frac{- 4 \pm \sqrt{76}}{2 \cdot 1}$

Rewrite $76$ as $2^{2} \cdot 19$ .

Factor $4$ out of $76$ .

$x = \frac{- 4 \pm \sqrt{4 (19)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 19}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{19}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 2 \sqrt{19}}{2}$

Simplify $\frac{- 4 \pm 2 \sqrt{19}}{2}$ .

$x = - 2 \pm \sqrt{19}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 2 \pm \sqrt{19}$

Decimal Form:

$x = 2.35889894 \dots, - 6.35889894 \dots$