Solve for a 4a^2-b^2=0

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

Step 1

Add $b^{2}$ to both sides of the equation.

$4 a^{2} = b^{2}$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

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

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

Step 3

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

$a = \pm \sqrt{\frac{b^{2}}{4}}$

Step 4

Simplify $\pm \sqrt{\frac{b^{2}}{4}}$ .

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

$a = \pm \sqrt{\frac{b^{2}}{2^{2}}}$

Rewrite $\frac{b^{2}}{2^{2}}$ as ${(\frac{b}{2})}^{2}$ .

$a = \pm \sqrt{{(\frac{b}{2})}^{2}}$

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

$a = \pm \frac{b}{2}$

Step 5

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.

$a = \frac{b}{2}$

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

$a = - \frac{b}{2}$

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

$a = \frac{b}{2}$

$a = - \frac{b}{2}$

$a = \frac{b}{2}$

$a = - \frac{b}{2}$