Solving quadratic equations

Definition. An equation that can be put into the form

a x^{2} + b x + c = 0

with

a \neq 0

is a quadratic equation. The unknown is

x

, and the coefficients are

a

b

, and

c

Because a quadratic equation has degree two, it can have at most two different solutions. These solutions may be real numbers or complex numbers. In this article, we will explore how to solve quadratic equations by a variety of methods: graphs, tables, factoring, and the quadratic formula.

Question. Is

x^{2} + 3 x = 2 x + 6

a quadratic equation? To find out, move all the terms to one side of the equation and then combine like terms.

\begin{aligned} x^{2} + 3 x & = 2 x + 6 \\ x^{2} + 3 x - 2 x - 6 & = 0 \\ x^{2} + x - 6 & = 0 \end{aligned}

Answer. Yes, it's a quadratic equation because we were able to put it in the form

a x^{2} + b x + c = 0

. The coefficients are

a = 1

b = 1

, and

c = - 6

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