Solve Using the Quadratic Formula b^2-4ac=0

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

Step 1

Add $4 a c$ to both sides of the equation.

$b^{2} = 4 a c$

Step 2

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

$b = \pm \sqrt{4 a c}$

Step 3

Simplify $\pm \sqrt{4 a c}$ .

Rewrite $4 a c$ as $2^{2} (a c)$ .

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

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

Add parentheses.

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

Pull terms out from under the radical.

$b = \pm 2 \sqrt{a c}$

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.

$b = 2 \sqrt{a c}$

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

$b = - 2 \sqrt{a c}$

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

$b = 2 \sqrt{a c}$

$b = - 2 \sqrt{a c}$

$b = 2 \sqrt{a c}$

$b = - 2 \sqrt{a c}$