Solve Using the Quadratic Formula x^2+14x+49=0

$x^{2} + 14 x + 49 = 0$

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 $a = 1$ , $b = 14$ , and $c = 49$ into the quadratic formula and solve for $x$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (1 \cdot 49)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $14$ to the power of $2$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 1 \cdot 49}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 49$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 49}}{2 \cdot 1}$

Multiply $- 4$ by $49$ .

$x = \frac{- 14 \pm \sqrt{196 - 196}}{2 \cdot 1}$

Subtract $196$ from $196$ .

$x = \frac{- 14 \pm \sqrt{0}}{2 \cdot 1}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{- 14 \pm \sqrt{0^{2}}}{2 \cdot 1}$

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

$x = \frac{- 14 \pm 0}{2 \cdot 1}$

$- 14$ plus or minus $0$ is $- 14$ .

$x = \frac{- 14}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 14}{2}$

Divide $- 14$ by $2$ .

$x = - 7$

Step 4

The final answer is the combination of both solutions.

$x = - 7$ Double roots