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Solve by factorising - OCR - GCSE Maths - Question 27 - 2019 - Paper 1

Question 27

Solve by factorising. $x^2 + 3x - 10 = 0$ $x = .........................$ or $x = .........................$

Worked Solution & Example Answer:Solve by factorising - OCR - GCSE Maths - Question 27 - 2019 - Paper 1

Step 1

Step 1: Rearrange the Equation

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Answer

We start with the equation: $x^2 + 3x - 10 = 0$ Our goal is to factor this quadratic equation.

Step 2

Step 2: Factor the Quadratic

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Answer

To factor the expression $x^2 + 3x - 10$ , we need to find two numbers that multiply to -10 (the constant term) and add to 3 (the coefficient of $x$ ). These two numbers are 5 and -2. Hence, we can write:

$x^2 + 3x - 10 = (x + 5)(x - 2) = 0$

Step 3

Step 3: Solve for x

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Answer

Now, we set each factor to zero:

$x + 5 = 0 \Rightarrow x = -5$
$x - 2 = 0 \Rightarrow x = 2$

Thus, the solutions are:

$x = -5$ or $x = 2$

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