Solve x^2 + 8x +3 = 0 by completing the square.

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Using the completing the square method:

1. Notice (x+4)2 = x2 + 8x +16 which differs from the question by a constant

2. So we can write: 

x2 + 8x + 3 = (x+4)2 - 13      (check this yourself if you don't see it immediately)

3. So from the question we get:

(x+4)-13 = 0

(x+4)= 13     (by adding 13)

x+4 = +-sqrt(13)    (square root remembering to include the +-)

x = -4 +-sqrt(13)      (subtracting 4)

So we have answers of:

x = - 4 + sqrt(13)

x = - 4 - sqrt(13)

which can both be checked by substitution into the original equation.

Lloyd S. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor

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