Solve for a 4a^2+4=72

$4 a^{2} + 4 = 72$

Step 1

Move all terms not containing $a$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$4 a^{2} = 72 - 4$

Subtract $4$ from $72$ .

$4 a^{2} = 68$

Step 2

Divide each term in $4 a^{2} = 68$ by $4$ and simplify.

Divide each term in $4 a^{2} = 68$ by $4$ .

$\frac{4 a^{2}}{4} = \frac{68}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a^{2}}{4} = \frac{68}{4}$

Divide $a^{2}$ by $1$ .

$a^{2} = \frac{68}{4}$

Simplify the right side.

Divide $68$ by $4$ .

$a^{2} = 17$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{17}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$a = \sqrt{17}$

Next, use the negative value of the $\pm$ to find the second solution.

$a = - \sqrt{17}$

The complete solution is the result of both the positive and negative portions of the solution.

$a = \sqrt{17}, - \sqrt{17}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \sqrt{17}, - \sqrt{17}$

Decimal Form:

$a = 4.12310562 \dots, - 4.12310562 \dots$