Question

timed problem
score: 2/10 current time: 64.4
which equation is equivalent to the given equation?
3x² + 12 = 15x

Explanation:

Step1: Rearrange the equation

We start with the given equation \(3x^{2}+12 = 15x\). To make it a standard quadratic equation form \(ax^{2}+bx + c=0\), we subtract \(15x\) from both sides.

$$3x^{2}-15x + 12=0$$

Step2: Simplify the equation (optional, but common)

We can divide the entire equation by 3 to simplify it. Dividing each term by 3:

$$\frac{3x^{2}}{3}-\frac{15x}{3}+\frac{12}{3}=0$$

Which simplifies to:

$$x^{2}-5x + 4=0$$

(If we factor this, we get \((x - 1)(x - 4)=0\), but the main task is to find an equivalent equation. The equation \(3x^{2}-15x + 12 = 0\) or \(x^{2}-5x + 4=0\) are equivalent to the original equation.)

Answer:

An equivalent equation is \(3x^{2}-15x + 12 = 0\) (or \(x^{2}-5x + 4=0\) after simplifying by dividing by 3).