Solving Quadratic Equations by Factorising
# Solving Quadratic Equations by Factorising

GCSE(F), GCSE(H),

Solutions for equations are found when an expression evaluates to zero. One method for solving a quadratic equation is by factorising (see Factorising Quadratic Expressions).

Rearrange the equation so that one side of the equation is equal to zero. Next, factorise the equation. Then find the *two* values of `x` that will solve the equation.

Note that not all quadratic expressions have a solution: for example, `x^2-3x+7` cannot be solved except by using advanced mathematics.

## Examples

1. Solve `x^2-4x-5=0`

Answer: `x=-1 text( and ) x=5`

Factorise the equation: `x^2-4x-5` can be rewritten as `(x+1)(x-5)=0`

Determine what values of `x` causes each set of brackets to equal zero: `(x+1)=0` when `x=-1`, and `(x-5) =0` when `x=5`.

The solutions are therefore `x=-1 text( and ) x=5`

Check: (-1)^{2} - 4(-1) - 5 =0, and 5^{2} - 4(5) - 5 = 0.

2. Solve `2x^2+7x=4`

Answer: `x=-1 text( and ) x=1`

Rearrange the equation so that one side of the equation equals zero: `2x^2 + 7x - 4 = 0`

Factorise the equation: `2x^2 + 2x - 4` can be rewritten as `(2x+1)(x-4)=0`

Determine what values of `x` causes each set of brackets to equal zero: `(2x+1)=0` when `x=-0.5`, and `(x-4) =0` when `x=4`.

The solutions are therefore `x=-0.5 text( and ) x=4`.

Our iOS app has over 1,000 questions to help you practice this and many other topics.

Available to download free on the

App Store.