Quadratic Formula Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Solve

x^2 - 5x + 6 = 0

by factoring.

1
Find two numbers that multiply to 6 and add to $-5$ : those are $-2$ and $-3$ .
2
Factor: $(x - 2)(x - 3) = 0$ .
3
Set each factor to zero: $x - 2 = 0$ or $x - 3 = 0$ .
4
Solutions: $x = 2$ or $x = 3$ .

Answer

x = 2 \text{ or } x = 3

Factoring works when you can find two numbers whose product equals the constant term and whose sum equals the coefficient of

x

. The zero product property then gives the solutions.

About Quadratic Formula

A formula giving the exact solutions to any quadratic equation $ax^2 + bx + c = 0$ directly from its three coefficients.

Solve [formula] using the quadratic formula.

Solve [formula] using the quadratic formula.

Solve [formula].

Solve [formula] and describe the solutions.