Solve Using the Quadratic Formula 2a^2-46a+252=0

$2 a^{2} - 46 a + 252 = 0$

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 $a = 2$ , $b = - 46$ , and $c = 252$ into the quadratic formula and solve for $a$ .

$\frac{46 \pm \sqrt{{(- 46)}^{2} - 4 \cdot (2 \cdot 252)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 46$ to the power of $2$ .

$a = \frac{46 \pm \sqrt{2116 - 4 \cdot 2 \cdot 252}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 252$ .

Multiply $- 4$ by $2$ .

$a = \frac{46 \pm \sqrt{2116 - 8 \cdot 252}}{2 \cdot 2}$

Multiply $- 8$ by $252$ .

$a = \frac{46 \pm \sqrt{2116 - 2016}}{2 \cdot 2}$

Subtract $2016$ from $2116$ .

$a = \frac{46 \pm \sqrt{100}}{2 \cdot 2}$

Rewrite $100$ as $10^{2}$ .

$a = \frac{46 \pm \sqrt{10^{2}}}{2 \cdot 2}$

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

$a = \frac{46 \pm 10}{2 \cdot 2}$

Multiply $2$ by $2$ .

$a = \frac{46 \pm 10}{4}$

Simplify $\frac{46 \pm 10}{4}$ .

$a = \frac{23 \pm 5}{2}$

Step 4

The final answer is the combination of both solutions.

$a = 14, 9$