Solve this equation, giving your answers correct to 1 decimal place - OCR - GCSE Maths - Question 20 - 2018 - Paper 1

Expanding both sides gives:

$5x - 15 + 3x + 6 = 2(x^2 - x - 6)$

This simplifies to:

$8x - 9 = 2x^2 - 2x - 12$

Rearranging all terms to one side results in:

$2x^2 - 10x + 3 = 0$

We can solve this equation using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Here, (a = 2), (b = -10), and (c = 3). Calculating the discriminant:

$b^2 - 4ac = (-10)^2 - 4(2)(3) = 100 - 24 = 76$

Thus, substituting into the formula gives us:

$x = \frac{10 \pm \sqrt{76}}{4}$

Calculating the two possible values:

$x_1 = \frac{10 + \sqrt{76}}{4} \approx 5.3$

$x_2 = \frac{10 - \sqrt{76}}{4} \approx -0.3$

Hence the answers are:

$x \approx -0.3$ or $x \approx 5.3$