Algebra 7

4 marks · Hard

Solve the quadratic equation by completing the square. Give your answers in surd form.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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x = \frac{5 \pm \sqrt{85}}{4}

Also accept: x = (5 + sqrt(85))/4, x = (5 - sqrt(85))/4

Common mistakes: Missing division by 2a at the end; Confusing plus/minus; Arithmetic error in rearrangement

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Marking points

M1 · 1 mark · Divides both sides by 2 and expresses in standard quadratic form suitable for completing the square.

M2 · 1 mark · Successfully completes the square, rearranges correctly to .

A1 · 1 mark · Correct surd value for square root step. (follow-through)

A2 · 1 mark · Both solutions given in fully simplified surd form: or equivalent. (follow-through)

Worked solution

Given:

Divide both sides by 2:

Add to both sides:

To complete the square: Take half of which is , then square it: .

So .