Solving Equations in Quadratic Form
Any equation in the form ax ^{2} + bx + c = 0 is said to be in quadratic form. This equation then can be solved by using the quadratic formula, by completing the square, or by factoring if it is factorable.
Example 1
Solve x ^{4} – 13 x ^{2} + 36 = 0 by (a) factoring and (b) applying the quadratic formula.

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By the zero product rule,

x ^{4} – 13 x ^{2} + 36 = 0
is equivalent to
When applying the quadratic formula to equations in quadratic form, you are solving for the variable name of the middle term. Thus, in this case,
Using the square root property,
Example 2
Solve by (a) factoring and (b) applying the quadratic formula.

In the last step on the right, must be a nonnegative value; therefore, has no solutions. The only solution is x = 36.

is equivalent to
When applying the quadratic formula to this quadratic form equation, you are solving for .
There is no solution for . Thus, x = 36 is the only solution.