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In a quadratic equation we have a variable and its square (x and x2). An equation
that contains an expression and the square of that expression is quadratic in form
if substituting a single variable for that expression results in a quadratic equation.
Equations that are quadratic in form can be solved by using methods for quadratic
equations.
Example
An equation quadratic in form
Solve (x + 15)2 - 3(x + 15) - 18 = 0
Solution
Note that x + 15 and (x + 15)2 both appear in the equation. Let a
= x + 15 and
substitute a for x + 15 in the equation:
(x + 15)2
- 3(x + 15) - 18
= 0
a2 - 3a - 18
= 0
(a - 6)(a + 3)
= 0
Factor.
a - 6
= 0
or
a + 3
= 0
a
= 6
or
a
= -3
x + 15
= 6
or
x + 15
= -3
Replace a by x + 15.
x
= -9
or
x
= -18
Check in the original equation. The solution set is {-18, -9}.
