Question

timed problem
score: 0/10 current time: 6.5
which equation is equivalent to the given equation?
-10x = 2x² - 28

Explanation:

Step1: Rearrange the equation

To find an equivalent equation, we can rearrange the given equation \(-10x = 2x^2 - 28\) into standard quadratic form \(ax^2+bx + c = 0\). First, move all terms to one side. Add \(10x\) to both sides and add \(28\) to both sides:
\(2x^2+10x - 28 = 0\)
We can also divide the entire equation by 2 to simplify:
\(x^2 + 5x - 14=0\)
Or, if we move terms to the other side, starting from \(-10x = 2x^2 - 28\), subtract \(2x^2\) and add \(28\) to both sides:
\(- 2x^2-10x + 28 = 0\)
Multiplying by - 1 gives \(2x^2 + 10x - 28=0\) (same as the first rearrangement after moving terms).

Step2: Check equivalent forms

For example, let's take the standard form. The given equation \(-10x = 2x^2 - 28\) can be rewritten as \(2x^2+10x - 28 = 0\) (by adding \(10x\) and \(28\) to both sides) or simplified by dividing by 2 to \(x^2 + 5x - 14 = 0\).

(Note: Since the problem didn't provide the options, we can show the process of finding an equivalent equation. If we assume common equivalent forms, the standard quadratic form or simplified form is equivalent. For example, \(2x^2 + 10x - 28 = 0\) or \(x^2+5x - 14 = 0\) are equivalent to \(-10x = 2x^2 - 28\))

Answer:

An equivalent equation is \(2x^2 + 10x - 28 = 0\) (or \(x^2+5x - 14 = 0\) after simplifying by dividing by 2)