Solve Using the Quadratic Formula x^2-19x+90=0

$x^{2} - 19 x + 90 = 0$

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 $a = 1$ , $b = - 19$ , and $c = 90$ into the quadratic formula and solve for $x$ .

$\frac{19 \pm \sqrt{{(- 19)}^{2} - 4 \cdot (1 \cdot 90)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 19$ to the power of $2$ .

$x = \frac{19 \pm \sqrt{361 - 4 \cdot 1 \cdot 90}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 90$ .

Multiply $- 4$ by $1$ .

$x = \frac{19 \pm \sqrt{361 - 4 \cdot 90}}{2 \cdot 1}$

Multiply $- 4$ by $90$ .

$x = \frac{19 \pm \sqrt{361 - 360}}{2 \cdot 1}$

Subtract $360$ from $361$ .

$x = \frac{19 \pm \sqrt{1}}{2 \cdot 1}$

Any root of $1$ is $1$ .

$x = \frac{19 \pm 1}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{19 \pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 10, 9$