Find All Complex Solutions x^2+34x-72=0

$x^{2} + 34 x - 72 = 0$

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 $a = 1$ , $b = 34$ , and $c = - 72$ into the quadratic formula and solve for $x$ .

$\frac{- 34 \pm \sqrt{34^{2} - 4 \cdot (1 \cdot - 72)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $34$ to the power of $2$ .

$x = \frac{- 34 \pm \sqrt{1156 - 4 \cdot 1 \cdot - 72}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 72$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 34 \pm \sqrt{1156 - 4 \cdot - 72}}{2 \cdot 1}$

Multiply $- 4$ by $- 72$ .

$x = \frac{- 34 \pm \sqrt{1156 + 288}}{2 \cdot 1}$

Add $1156$ and $288$ .

$x = \frac{- 34 \pm \sqrt{1444}}{2 \cdot 1}$

Rewrite $1444$ as $38^{2}$ .

$x = \frac{- 34 \pm \sqrt{38^{2}}}{2 \cdot 1}$

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

$x = \frac{- 34 \pm 38}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 34 \pm 38}{2}$

Simplify $\frac{- 34 \pm 38}{2}$ .

$x = - 17 \pm 19$

Step 4

The final answer is the combination of both solutions.

$x = 2, - 36$