GCSE Mathematics (9-1)
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    12.6 Completing the square — Practise with help

    Warm-up: remember

    Answer these from memory. Do not look back at the section.

    1. Expand (x+5)2(x+5)^2.
    2. Solve y2=9y^2=9.
    Check the warm-up
    1. x2+10x+25x^2+10x+25.
    2. y=3y=3 or y=−3y=-3.

    If an answer differs, revisit Section 8.3 for expanding brackets and Section 3.2 for square roots.

    Practise with help

    1. Complete the square for x2−8x+3x^2-8x+3.

    Hint

    Take half of −8-8, then square it.

    Next step

    Use the hint to write the next algebra line. Then finish the calculation before opening the full working.

    Full working

    Half is −4-4 and its square is 1616: x2−8x+3=(x−4)2−13x^2-8x+3=(x-4)^2-13.

    Choose a method: factorise x2+7x+10x^2+7x+10. Which method applies, and why?

    Full working

    Factorisation applies because the expression is a monic quadratic with integer factors: x2+7x+10=(x+5)(x+2)x^2+7x+10=(x+5)(x+2).

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