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Which equation is equivalent to the given equation?%0D%0A12, x, plus, 180, equals, 3, x, squared%0D%0A12x+180=3x %0D%0A2%0D%0A %0D%0AAnswer%0D%0A3, x, squared, plus, 12, x, plus, 180, equals, 0%0D%0A3x %0D%0A2%0D%0A +12x+180=0%0D%0A3, x, squared, plus, 12, x, minus, 180, equals, 0%0D%0A3x %0D%0A2%0D%0A +12x−180=0%0D%0A3, x, squared, minus, 12, x, minus, 180, equals, 0%0D%0A3x %0D%0A2%0D%0A −12x−180=0%0D%0A3, x, squared, minus, 12, x, plus, 180, equals, 0%0D%0A3x %0D%0A2%0D%0A −12x+180=0

1 answer

Let's analyze the given equation:

\[ 12x + 180 = 3x^2 \]

To find an equivalent equation, we can rearrange it into standard quadratic form, which is typically written as:

\[ ax^2 + bx + c = 0 \]

Starting from the given equation:

\[ 12x + 180 = 3x^2 \]

We want to get everything on one side of the equation:

  1. Subtract \(12x\) and \(180\) from both sides:

\[ 0 = 3x^2 - 12x - 180 \]

Now, we can rewrite this as:

\[ 3x^2 - 12x - 180 = 0 \]

This matches with one of the options you provided:

3x² - 12x - 180 = 0

So the correct equivalent equation is:

3x² - 12x - 180 = 0.