# Solving Quadratic Equations Using Square Roots

The general form of a quadratic equation is:

$a{x}^{2}+bx+c=0$

If $b=0$ , the equation can solved by putting it in the form

${x}^{2}=d$

for some new constant
$d$
, and taking the
square root
of both sides. (Both positive and negative square roots count. because we want
**
all
**
of the numbers that solve the equation.) Again, this easy method of solution only works in the special case when
$b=0$
.

**
Example:
**

Solve for $x$ .

$8{x}^{2}+4=76$

Put the equation into the form ${x}^{2}=d$ . Start by subtracting $4$ from both sides.

$8{x}^{2}=72$

Divide both sides by $8$ .

${x}^{2}=9$

Take square roots of both sides.

$x=3\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-3$

There are two solutions to the equation.