Solve $x^2 = 5x + 24$ - Edexcel - GCSE Maths - Question 9 - 2021 - Paper 1

In the standard quadratic form $ax^2 + bx + c = 0$, identify the coefficients:

• $a = 1$
• $b = -5$
• $c = -24$

Now apply the quadratic formula:

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

Substituting the values of $a$, $b$, and $c$:

$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-24)}}{2(1)}$

This simplifies to:

$x = \frac{5 \pm \sqrt{25 + 96}}{2}$

Continue simplifying:

$x = \frac{5 \pm \sqrt{121}}{2}$

Which leads to: $x = \frac{5 \pm 11}{2}$

Thus, the solutions are:

• $x = \frac{16}{2} = 8$
• $x = \frac{-6}{2} = -3$