Write as a Function of c 2p^2-8p+c=0

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

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 $a = 2$ , $b = - 8$ , and $c = c$ into the quadratic formula and solve for $p$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

Multiply $- 4$ by $2$ .

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

Factor $8$ out of $64 - 8 c$ .

Factor $8$ out of $64$ .

$p = \frac{8 \pm \sqrt{8 (8) - 8 c}}{2 \cdot 2}$

Factor $8$ out of $- 8 c$ .

$p = \frac{8 \pm \sqrt{8 (8) + 8 (- c)}}{2 \cdot 2}$

Factor $8$ out of $8 (8) + 8 (- c)$ .

$p = \frac{8 \pm \sqrt{8 (8 - c)}}{2 \cdot 2}$

Rewrite $8 (8 - c)$ as $2^{2} \cdot (2 (8 - c))$ .

Factor $4$ out of $8$ .

$p = \frac{8 \pm \sqrt{4 (2) (8 - c)}}{2 \cdot 2}$

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

$p = \frac{8 \pm \sqrt{2^{2} \cdot (2 (8 - c))}}{2 \cdot 2}$

Add parentheses.

$p = \frac{8 \pm \sqrt{2^{2} \cdot (2 (8 - c))}}{2 \cdot 2}$

Pull terms out from under the radical.

$p = \frac{8 \pm 2 \sqrt{2 (8 - c)}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$p = \frac{8 \pm 2 \sqrt{2 (8 - c)}}{4}$

Simplify $\frac{8 \pm 2 \sqrt{2 (8 - c)}}{4}$ .

$p = \frac{4 \pm \sqrt{2 (8 - c)}}{2}$

Step 4

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

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

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

Multiply $- 4$ by $2$ .

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

Factor $8$ out of $64 - 8 c$ .

Factor $8$ out of $64$ .

$p = \frac{8 \pm \sqrt{8 (8) - 8 c}}{2 \cdot 2}$

Factor $8$ out of $- 8 c$ .

$p = \frac{8 \pm \sqrt{8 (8) + 8 (- c)}}{2 \cdot 2}$

Factor $8$ out of $8 (8) + 8 (- c)$ .

$p = \frac{8 \pm \sqrt{8 (8 - c)}}{2 \cdot 2}$

Rewrite $8 (8 - c)$ as $2^{2} \cdot (2 (8 - c))$ .

Factor $4$ out of $8$ .

$p = \frac{8 \pm \sqrt{4 (2) (8 - c)}}{2 \cdot 2}$

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

$p = \frac{8 \pm \sqrt{2^{2} \cdot (2 (8 - c))}}{2 \cdot 2}$

Add parentheses.

$p = \frac{8 \pm \sqrt{2^{2} \cdot (2 (8 - c))}}{2 \cdot 2}$

Pull terms out from under the radical.

$p = \frac{8 \pm 2 \sqrt{2 (8 - c)}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$p = \frac{8 \pm 2 \sqrt{2 (8 - c)}}{4}$

Simplify $\frac{8 \pm 2 \sqrt{2 (8 - c)}}{4}$ .

$p = \frac{4 \pm \sqrt{2 (8 - c)}}{2}$

Change the $\pm$ to $+$ .

$p = \frac{4 + \sqrt{2 (8 - c)}}{2}$

Step 5

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

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

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

Multiply $- 4$ by $2$ .

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

Factor $8$ out of $64 - 8 c$ .

Factor $8$ out of $64$ .

$p = \frac{8 \pm \sqrt{8 (8) - 8 c}}{2 \cdot 2}$

Factor $8$ out of $- 8 c$ .

$p = \frac{8 \pm \sqrt{8 (8) + 8 (- c)}}{2 \cdot 2}$

Factor $8$ out of $8 (8) + 8 (- c)$ .

$p = \frac{8 \pm \sqrt{8 (8 - c)}}{2 \cdot 2}$

Rewrite $8 (8 - c)$ as $2^{2} \cdot (2 (8 - c))$ .

Factor $4$ out of $8$ .

$p = \frac{8 \pm \sqrt{4 (2) (8 - c)}}{2 \cdot 2}$

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

$p = \frac{8 \pm \sqrt{2^{2} \cdot (2 (8 - c))}}{2 \cdot 2}$

Add parentheses.

$p = \frac{8 \pm \sqrt{2^{2} \cdot (2 (8 - c))}}{2 \cdot 2}$

Pull terms out from under the radical.

$p = \frac{8 \pm 2 \sqrt{2 (8 - c)}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$p = \frac{8 \pm 2 \sqrt{2 (8 - c)}}{4}$

Simplify $\frac{8 \pm 2 \sqrt{2 (8 - c)}}{4}$ .

$p = \frac{4 \pm \sqrt{2 (8 - c)}}{2}$

Change the $\pm$ to $-$ .

$p = \frac{4 - \sqrt{2 (8 - c)}}{2}$

Step 6

The final answer is the combination of both solutions.

$p = \frac{4 + \sqrt{2 (8 - c)}}{2}$

$p = \frac{4 - \sqrt{2 (8 - c)}}{2}$

Write as a Function of c 2p^2-8p+c=0

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