Question

the solution to $x^2 - 10x = 24$ is
7 or $-7$
$2 + 2i$ or $2 - 2i$
12 or $-2$

Explanation:

Step1: Rearrange the equation

We start with the equation \(x^2 - 10x = 24\). To solve this quadratic equation, we first rewrite it in standard form \(ax^2+bx + c = 0\) by subtracting 24 from both sides:
\(x^2 - 10x - 24=0\)

Step2: Factor the quadratic equation

We need to find two numbers that multiply to \(- 24\) and add up to \(-10\). The numbers are \(-12\) and \(2\) because \((-12)\times2=-24\) and \(-12 + 2=-10\). So we can factor the quadratic as:
\((x - 12)(x+ 2)=0\)

Step3: Solve for \(x\)

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So we set each factor equal to zero:

• If \(x - 12=0\), then \(x = 12\).
• If \(x + 2=0\), then \(x=-2\).

Answer:

12 or -2