Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 4
Question 16
Solve by factorisation.
$$2x^2 - 19x - 33 = 0$$
Worked Solution & Example Answer:Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 4
Step 1
Step 1: Factor the Quadratic Equation
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Answer
To solve the equation (2x^2 - 19x - 33 = 0) by factorisation, we start by finding two numbers that multiply to (2 \times -33 = -66) and add to (-19). The numbers (-22) and (+3) satisfy these conditions.
Now we can rewrite the middle term:
2x2−22x+3x−33=0
Next, we group the terms:
2x(x−11)+3(x−11)=0
Step 2
Step 2: Solve for x
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Answer
Now we factor out ((x - 11)
(2x+3)(x−11)=0
Setting each factor to zero gives:
(2x + 3 = 0)
This simplifies to (2x = -3) hence (x = -\frac{3}{2})
(x - 11 = 0)
This simplifies to (x = 11)
Thus, the solutions are:
[ x = -\frac{3}{2} \text{ or } x = 11 ]
