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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

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