How to Solve Quadratic Equations Without a Linear Term

Equations with powers, or quadratic equations, are really fun to solve when you don’t have a first degree term (a number on its own).

You should be comfortable with square roots to be able to find the answer without any aids. You should also have control over change sides/change sign and know how to get rid of a number in front of $x$ .

Rule

Equations with Powers

The equation

a x^{2} + b = 0

has the solutions

x = \pm \sqrt{- \frac{b}{a}} .

If you have a problem where the number inside the square root is negative, the equation has no real solution, because you can’t take the square root of a negative number using normal means.

Think About This

Why do you think we can’t take the square root of a negative number?

The square root is defined as $\sqrt{a^{2}} = \pm a$ . Any number raised to the power of $2$ become a positive number because $- \cdot - = +$ . This means that $a^{2} \geq 0$ , even if $a < 0$ .