Question

imed problem
score: 3/10 current time: 66.5
which equation is equivalent to the given equation?
54x - 243 = 3x²
answer
3x² + 54x - 243 = 0 3x² - 54x - 243 = 0 3x² + 54x + 243 = 0 3x² - 54x + 243 = 0

Explanation:

Step1: Rearrange the given equation

We start with the equation \(54x - 243 = 3x^{2}\). To get all terms on one side, we subtract \(54x\) and add \(243\) to both sides (or move all terms to the right side by subtracting \(54x\) and adding \(243\) to both sides, but a more standard way is to set the equation to zero in standard quadratic form \(ax^{2}+bx + c = 0\)). Let's move all terms to the right side:
Subtract \(54x\) from both sides: \( - 243=3x^{2}-54x\)
Then add \(243\) to both sides: \(0 = 3x^{2}-54x + 243\)
Which can be rewritten as \(3x^{2}-54x + 243 = 0\)

Step2: Verify the equivalent equation

We check each option:

• Option 1: \(3x^{2}+54x - 243 = 0\) is not equivalent as the signs of \(54x\) and \(243\) are wrong.
• Option 2: \(3x^{2}-54x - 243 = 0\) has the wrong sign for \(243\).
• Option 3: \(3x^{2}+54x + 243 = 0\) has wrong signs for \(54x\) and \(243\).
• Option 4: \(3x^{2}-54x + 243 = 0\) matches our rearranged equation.

Answer:

\(3x^{2}-54x + 243 = 0\) (the fourth option: \(3x^{2}-54x + 243 = 0\))