Solve Using the Quadratic Formula x^2+17x+42=0

$x^{2} + 17 x + 42 = 0$

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 $a = 1$ , $b = 17$ , and $c = 42$ into the quadratic formula and solve for $x$ .

$\frac{- 17 \pm \sqrt{17^{2} - 4 \cdot (1 \cdot 42)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $17$ to the power of $2$ .

$x = \frac{- 17 \pm \sqrt{289 - 4 \cdot 1 \cdot 42}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 42$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 17 \pm \sqrt{289 - 4 \cdot 42}}{2 \cdot 1}$

Multiply $- 4$ by $42$ .

$x = \frac{- 17 \pm \sqrt{289 - 168}}{2 \cdot 1}$

Subtract $168$ from $289$ .

$x = \frac{- 17 \pm \sqrt{121}}{2 \cdot 1}$

Rewrite $121$ as $11^{2}$ .

$x = \frac{- 17 \pm \sqrt{11^{2}}}{2 \cdot 1}$

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

$x = \frac{- 17 \pm 11}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 17 \pm 11}{2}$

Step 4

The final answer is the combination of both solutions.

$x = - 3, - 14$