Solve Using the Quadratic Formula x^2+18x+74=0

$x^{2} + 18 x + 74 = 0$

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 $a = 1$ , $b = 18$ , and $c = 74$ into the quadratic formula and solve for $x$ .

$\frac{- 18 \pm \sqrt{18^{2} - 4 \cdot (1 \cdot 74)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $18$ to the power of $2$ .

$x = \frac{- 18 \pm \sqrt{324 - 4 \cdot 1 \cdot 74}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 74$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 18 \pm \sqrt{324 - 4 \cdot 74}}{2 \cdot 1}$

Multiply $- 4$ by $74$ .

$x = \frac{- 18 \pm \sqrt{324 - 296}}{2 \cdot 1}$

Subtract $296$ from $324$ .

$x = \frac{- 18 \pm \sqrt{28}}{2 \cdot 1}$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$x = \frac{- 18 \pm \sqrt{4 (7)}}{2 \cdot 1}$

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

$x = \frac{- 18 \pm \sqrt{2^{2} \cdot 7}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 18 \pm 2 \sqrt{7}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 18 \pm 2 \sqrt{7}}{2}$

Simplify $\frac{- 18 \pm 2 \sqrt{7}}{2}$ .

$x = - 9 \pm \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 9 \pm \sqrt{7}$

Decimal Form:

$x = - 6.35424868 \dots, - 11.64575131 \dots$