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Solve by factorisation - OCR - GCSE Maths - Question 15 - 2019 - Paper 6

Question 15

Solve by factorisation. 5x² + 7x + 2 = 0 x = ......................... or x = .........................

Worked Solution & Example Answer:Solve by factorisation - OCR - GCSE Maths - Question 15 - 2019 - Paper 6

Step 1

Factor the quadratic equation

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Answer

To factor the quadratic equation 5x² + 7x + 2, we first look for two numbers that multiply to the product of the coefficient of x² (5) and the constant term (2), which is 10, and add up to the coefficient of x (7). These numbers are 5 and 2.

We can rewrite the equation as:

5x² + 5x + 2x + 2 = 0.

Next, we group the terms:

(5x² + 5x) + (2x + 2) = 0.

Factoring out common factors, we have:

5x(x + 1) + 2(x + 1) = 0.

Now we can factor by grouping:

(5x + 2)(x + 1) = 0.

Step 2

Solve for x

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Answer

Setting each factor to zero gives us the possible solutions:

5x + 2 = 0

Solving for x:

5x = -2

x = -\frac{2}{5}

x + 1 = 0

Solving for x:

x = -1

Thus, the solutions to the equation are:

x = -\frac{2}{5} \text{ or } x = -1.

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