GCSE OCR Maths Solving quadratic equations: Solve. $$x^2 - 6x + 15 = 3x

Solve. $$x^2 - 6x + 15 = 3x - 5$$ Expand and simplify - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Question 13

Solve. $$x^2 - 6x + 15 = 3x - 5$$ Expand and simplify. $$(2x - 1)(x + 5)(3x - 2)$$

Worked Solution & Example Answer:Solve. $$x^2 - 6x + 15 = 3x - 5$$ Expand and simplify - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Step 1

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Answer

First, we rearrange the equation by moving all terms to one side:

$x^2 - 6x - 3x + 15 + 5 = 0$

This simplifies to:

$x^2 - 9x + 20 = 0$

Next, we can factor the quadratic equation:

$x^2 - 9x + 20 = (x - 5)(x - 4) = 0$

Setting each factor equal to zero gives us:

$x - 5 = 0 \Rightarrow x = 5$ $x - 4 = 0 \Rightarrow x = 4$

Therefore, the solutions are:

$x = 5 \text{ or } x = 4$

Step 2

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Answer

We start by expanding the first two factors:

$(2x - 1)(x + 5) = 2x^2 + 10x - x - 5 = 2x^2 + 9x - 5$

Now, we will multiply this result by the third factor:

$(2x^2 + 9x - 5)(3x - 2)$

Expanding this gives us:

Combining these results:

$6x^3 + (-4x^2 + 27x^2) + (-18x - 15x) + 10 = 6x^3 + 23x^2 - 33x + 10$

Thus, the final simplified expression is:

$6x^3 + 23x^2 - 33x + 10$