Solve Using the Quadratic Formula x^2-18x=19

$x^{2} - 18 x = 19$

Step 1

Subtract $19$ from both sides of the equation.

$x^{2} - 18 x - 19 = 0$

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 $a = 1$ , $b = - 18$ , and $c = - 19$ into the quadratic formula and solve for $x$ .

$\frac{18 \pm \sqrt{{(- 18)}^{2} - 4 \cdot (1 \cdot - 19)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{18 \pm \sqrt{324 - 4 \cdot 1 \cdot - 19}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 19$ .

Multiply $- 4$ by $1$ .

$x = \frac{18 \pm \sqrt{324 - 4 \cdot - 19}}{2 \cdot 1}$

Multiply $- 4$ by $- 19$ .

$x = \frac{18 \pm \sqrt{324 + 76}}{2 \cdot 1}$

Add $324$ and $76$ .

$x = \frac{18 \pm \sqrt{400}}{2 \cdot 1}$

Rewrite $400$ as $20^{2}$ .

$x = \frac{18 \pm \sqrt{20^{2}}}{2 \cdot 1}$

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

$x = \frac{18 \pm 20}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{18 \pm 20}{2}$

Simplify $\frac{18 \pm 20}{2}$ .

$x = 9 \pm 10$

Step 5

The final answer is the combination of both solutions.

$x = 19, - 1$