Question

x² = -15 - 8x

Explanation:

Step1: Rearrange the equation

First, we need to rewrite the given equation \(x^{2} = -15 - 8x\) in standard quadratic form \(ax^{2}+bx + c = 0\). By adding \(15\) and \(8x\) to both sides, we get:
\(x^{2}+8x + 15 = 0\)

Step2: Factor the quadratic equation

We look for two numbers that multiply to \(15\) (the constant term \(c\)) and add up to \(8\) (the coefficient of \(x\), which is \(b\)). The numbers \(3\) and \(5\) satisfy this because \(3\times5 = 15\) and \(3 + 5 = 8\). So we can factor the quadratic as:
\((x + 3)(x + 5)=0\)

Step3: Solve for \(x\)

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

• For \(x+3 = 0\), subtracting \(3\) from both sides gives \(x=-3\).
• For \(x + 5 = 0\), subtracting \(5\) from both sides gives \(x=-5\).

Answer:

The solutions of the equation \(x^{2}=-15 - 8x\) are \(x=-3\) and \(x=-5\).