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Solve by factorising - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Question 18

Solve by factorising. $x^{2} + 9x + 20 = 0$ $x = .................... or x = .................... [3]

Worked Solution & Example Answer:Solve by factorising - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Step 1

Step 1: Factor the quadratic equation

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Answer

To factor the quadratic equation $x^{2} + 9x + 20 = 0$ , we need two numbers that multiply to 20 (the constant term) and add up to 9 (the coefficient of the linear term). The numbers 4 and 5 satisfy these conditions because:

$4 \times 5 = 20$

and

$4 + 5 = 9$

Thus, we can rewrite the equation as:

$(x + 4)(x + 5) = 0$

Step 2

Step 2: Set each factor to zero

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Answer

Now that we have factored the equation, we set each factor equal to zero:

$x + 4 = 0$ $x + 5 = 0$

Step 3

Step 3: Solve for x

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Answer

Solving these equations gives:

For $x + 4 = 0$ : $x = -4$

For $x + 5 = 0$ : $x = -5$

Thus, the solutions are:

$x = -4$ or $x = -5$ .

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