Solve Using the Quadratic Formula x(x-17)+72=0

$x (x - 17) + 72 = 0$

Step 1

Simplify the left side.

Simplify each term.

Apply the distributive property.

$x \cdot x + x \cdot - 17 + 72 = 0$

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 17 + 72 = 0$

Move $- 17$ to the left of $x$ .

$x^{2} - 17 x + 72 = 0$

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 $a = 1$ , $b = - 17$ , and $c = 72$ into the quadratic formula and solve for $x$ .

$\frac{17 \pm \sqrt{{(- 17)}^{2} - 4 \cdot (1 \cdot 72)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{17 \pm \sqrt{289 - 4 \cdot 1 \cdot 72}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{17 \pm \sqrt{289 - 4 \cdot 72}}{2 \cdot 1}$

Multiply $- 4$ by $72$ .

$x = \frac{17 \pm \sqrt{289 - 288}}{2 \cdot 1}$

Subtract $288$ from $289$ .

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

Any root of $1$ is $1$ .

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

Multiply $2$ by $1$ .

$x = \frac{17 \pm 1}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 9, 8$