Solve Using the Quadratic Formula 4a^2-8=a

$4 a^{2} - 8 = a$

Step 1

Subtract $a$ from both sides of the equation.

$4 a^{2} - 8 - a = 0$

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 $a = 4$ , $b = - 1$ , and $c = - 8$ into the quadratic formula and solve for $a$ .

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

Step 4

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

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

Multiply $- 4 \cdot 4 \cdot - 8$ .

Multiply $- 4$ by $4$ .

$a = \frac{1 \pm \sqrt{1 - 16 \cdot - 8}}{2 \cdot 4}$

Multiply $- 16$ by $- 8$ .

$a = \frac{1 \pm \sqrt{1 + 128}}{2 \cdot 4}$

Add $1$ and $128$ .

$a = \frac{1 \pm \sqrt{129}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$a = \frac{1 \pm \sqrt{129}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1 \pm \sqrt{129}}{8}$

Decimal Form:

$a = 1.54472708 \dots, - 1.29472708 \dots$