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Solving Quadratic Equations Using Square Roots

The general form of a quadratic equation is:

a x 2 + b x + 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     or     − 3

There are two solutions to the equation.