Question

Solve for x:x^2 – 10x = 24

Answer 1

x = -2 and x = 12

Step-by-step explanation

We are given the equation:

`\begin{gathered} x^2\text{ - 10x = 24} \\ \Rightarrow x^2\text{ - 10x - 24 = 0} \end{gathered}`

This is a quadratic equation.

To solve it we have to find two numbers such that they add up to -10 and their product is -24.

The two numbers we need are:

-12 and +2

So, we now have that:

`\begin{gathered} x^2\text{ - 12x + 2x - 24 = 0} \\ \text{Factorise:} \\ x(x\text{ - 12) + 2(x - 12) = 0} \\ (x\text{ + 2)(x - 12) = 0} \\ \Rightarrow\text{ x = -2 and x = 12} \end{gathered}`

Those are the values of x.