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 52 - 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`.