Question

timed problem
score: 1/10 current time: 37.5
which equation is equivalent to the given equation?
-3x² + 12 = -9x

Explanation:

Step1: Rearrange the equation

First, we want to get all terms on one side to form a standard quadratic equation. Add \(9x\) to both sides of the equation \(-3x^{2}+12 = - 9x\).
We get \(-3x^{2}+9x + 12=0\).

Step2: Simplify the equation (optional, divide by - 3)

We can divide the entire equation by \(-3\) to simplify it. Dividing each term by \(-3\):
\(\frac{-3x^{2}}{-3}+\frac{9x}{-3}+\frac{12}{-3}=0\)
Which simplifies to \(x^{2}-3x - 4 = 0\).
(Alternatively, we could also factor the original rearranged equation. Let's check factoring the equation \(-3x^{2}+9x + 12 = 0\). First, factor out \(-3\): \(-3(x^{2}-3x - 4)=0\), and then factor the quadratic inside the parentheses: \(x^{2}-3x - 4=(x - 4)(x + 1)\), so the equation becomes \(-3(x - 4)(x + 1)=0\), which is also equivalent to the original equation. But the most common equivalent form after simplifying is \(x^{2}-3x - 4 = 0\) or other forms obtained by multiplying or dividing by a non - zero constant or factoring.)

Since the problem just asks for an equivalent equation, one equivalent equation is \(x^{2}-3x - 4 = 0\) (or \(-3x^{2}+9x + 12 = 0\), or \(3x^{2}-9x - 12 = 0\) by multiplying the equation \(x^{2}-3x - 4 = 0\) by 3, etc.)

Answer:

One equivalent equation is \(x^{2}-3x - 4 = 0\) (or other equivalent forms like \(-3x^{2}+9x + 12 = 0\), \(3x^{2}-9x - 12 = 0\), \((x - 4)(x + 1)=0\) etc.)