Academic Skills Advice
Summary
Solving Quadratics
There are 3 ways of solving a quadratic. Remember these are just different ways of
getting the same result and you can choose which you prefer to use. It is a good idea to
learn and practice all 3 methods as often one method is easier to use (or more appropriate)
than another.
Factorise
Into 2 brackets:
Formula
(𝑥 − 5)(𝑥 + 7) = 0
𝑥=
𝑥 = 5 𝑜𝑟 𝑥 = −7
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
−2 ± √22 − 4 × 1 × −35
2×1
𝑥=
−2 ± √144
2
𝑥=
𝑥 2 + 2𝑥 − 35 = 0
−2 ± 12
2
𝑥 = 5 𝑜𝑟 𝑥 = −7
The number under the square root sign (144)
tells you whether the quadratic can be solved.
If the number is –ve then it can’t be square
rooted so there is no real solution.
Completing the Square
(Find the squared bracket by using half of the 𝑥 coefficient)
(𝑥 + 1)2 − 12 − 35 = 0
(𝑥 + 1)2 − 36 = 0
(𝑥 + 1)2 = 36
𝑥 + 1 = ±√36
𝑥 = ±6 − 1
𝑥 = 5 𝑜𝑟 𝑥 = −7
© H Jackson 2011 / ACADEMIC SKILLS
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