Solve Using the Quadratic Formula x^2+6=-7x

$x^{2} + 6 = - 7 x$

Step 1

Add $7 x$ to both sides of the equation.

$x^{2} + 6 + 7 x = 0$

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 $a = 1$ , $b = 7$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot 6)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot 6}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 6$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 6}}{2 \cdot 1}$

Multiply $- 4$ by $6$ .

$x = \frac{- 7 \pm \sqrt{49 - 24}}{2 \cdot 1}$

Subtract $24$ from $49$ .

$x = \frac{- 7 \pm \sqrt{25}}{2 \cdot 1}$

Rewrite $25$ as $5^{2}$ .

$x = \frac{- 7 \pm \sqrt{5^{2}}}{2 \cdot 1}$

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

$x = \frac{- 7 \pm 5}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm 5}{2}$

Step 5

The final answer is the combination of both solutions.

$x = - 1, - 6$