Solve Using the Quadratic Formula p^2-8p+21=6

$p^{2} - 8 p + 21 = 6$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $6$ from both sides of the equation.

$p^{2} - 8 p + 21 - 6 = 0$

Subtract $6$ from $21$ .

$p^{2} - 8 p + 15 = 0$

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 $a = 1$ , $b = - 8$ , and $c = 15$ into the quadratic formula and solve for $p$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 15)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$p = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 15}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 15$ .

Multiply $- 4$ by $1$ .

$p = \frac{8 \pm \sqrt{64 - 4 \cdot 15}}{2 \cdot 1}$

Multiply $- 4$ by $15$ .

$p = \frac{8 \pm \sqrt{64 - 60}}{2 \cdot 1}$

Subtract $60$ from $64$ .

$p = \frac{8 \pm \sqrt{4}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$p = \frac{8 \pm \sqrt{2^{2}}}{2 \cdot 1}$

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

$p = \frac{8 \pm 2}{2 \cdot 1}$

Multiply $2$ by $1$ .

$p = \frac{8 \pm 2}{2}$

Simplify $\frac{8 \pm 2}{2}$ .

$p = 4 \pm 1$

Step 5

The final answer is the combination of both solutions.

$p = 5, 3$