Solve Using the Quadratic Formula p^2-5p+17=4p

$p^{2} - 5 p + 17 = 4 p$

Step 1

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

Subtract $4 p$ from both sides of the equation.

$p^{2} - 5 p + 17 - 4 p = 0$

Subtract $4 p$ from $- 5 p$ .

$p^{2} - 9 p + 17 = 0$

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 $a = 1$ , $b = - 9$ , and $c = 17$ into the quadratic formula and solve for $p$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (1 \cdot 17)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$p = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 17$ .

Multiply $- 4$ by $1$ .

$p = \frac{9 \pm \sqrt{81 - 4 \cdot 17}}{2 \cdot 1}$

Multiply $- 4$ by $17$ .

$p = \frac{9 \pm \sqrt{81 - 68}}{2 \cdot 1}$

Subtract $68$ from $81$ .

$p = \frac{9 \pm \sqrt{13}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$p = \frac{9 \pm \sqrt{13}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{9 \pm \sqrt{13}}{2}$

Decimal Form:

$p = 6.30277563 \dots, 2.69722436 \dots$