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Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 4

Question 16

Solve by factorisation. $$2x^2 - 19x - 33 = 0$$ x = ............................ or x = ............................

Worked Solution & Example Answer:Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 4

Step 1

Factor the equation

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Answer

First, we need to rewrite the quadratic equation in a factorable form. We look for two numbers that multiply to (2 \times -33 = -66) and add up to (-19). The correct factors are (-22) and (+3).

Thus, we can rewrite the equation as:

$2x^2 - 22x + 3x - 33 = 0$

Step 2

Group and factor

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Answer

Next, we group the terms:

$(2x^2 - 22x) + (3x - 33) = 0$

Factor out common terms:

$2x(x - 11) + 3(x - 11) = 0$

Step 3

Complete the factorisation

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Answer

Now, we can combine the factors:

$(2x + 3)(x - 11) = 0$

This gives us two equations to solve:

(2x + 3 = 0) leads to (x = -\frac{3}{2})
(x - 11 = 0) leads to (x = 11)

Thus, the solutions are:

$x = -\frac{3}{2} \text{ or } x = 11$

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