    ### Solving quadratics of the form x2 + bx + c = 0 by factorising first

This means find the values of x where the quadratic x2 + bx + c = 0 This can be done as follows:

 i. Factorise x2 + bx + c = 0 into the form (x + n)(x + q)This has already been shown in Factorising Quadratics − 1 ii. So (x + n)(x + q) = 0 iii. The values in either of the above brackets must equal to 0, as brackets means multiply and anything multipled by 0 is equal to 0. So:
 x + n = 0 => x = −n or x + q = 0 => x = −q
• #### Example 1.   Solve x2 + 7x + 6 = 0

•  i. From example 1 in Factorising Quadratics − 1 the factors are: (x + 1)(x + 6) ii. So (x + 1)(x + 6) = 0
 iii. x + 1 = 0 => x = −1 Or x + 6 = 0 => x = −6

• #### Example 2.   Solve x2 − 11x + 30 = 0

•  i. From example 2 in Factorising Quadratics − 1 the factors are: (x − 5)(x − 6) ii. So (x − 5)(x − 6) = 0
 iii. x − 5 = 0 => x = 5 Or x − 6 = 0 => x = 6

• #### Example 3.   Solve x2 + 2x − 8 = 0

•  i. From example 3 in Factorising Quadratics − 1 the factors are: (x + 4)(x − 2) ii. So (x + 4)(x − 2) = 0
 iii. x + 4 = 0 => x = −4 Or x − 2 = 0 => x = 2

• #### Example 4.   Solve x2 − 5x − 24 = 0

•  i. From example 4 in Factorising Quadratics − 1 the factors are: (x + 3)(x − 8) ii. So (x + 3)(x − 8) = 0
 iii. x + 3 = 0 => x = −3 Or x − 8 = 0 => x = 8

#### Remember:Find the values of x where x2 + bx + c = 0 is the same as solve x2 + bx + c = 0 to:  