Question

Can you find the standard form of the quadratic equation 12x^2 = 36x and then solve for x by factoring out the greatest common factor?

Answer 1

To find the standard form of the quadratic equation given by \(12x^2 = 36x\), we start by rearranging it into the standard form \(ax^2 + bx + c = 0\).

1. Move all terms to one side of the equation:
\[
12x^2 - 36x = 0
\]

Next, we can factor out the greatest common factor (GCF) from the left-hand side. The GCF of \(12x^2\) and \(-36x\) is \(12x\):

2. Factor out \(12x\):
\[
12x(x - 3) = 0
\]

Now, we can set each factor equal to zero to solve for \(x\):

3. Set each factor to zero:
- First factor:
\[
12x = 0 \quad \Rightarrow \quad x = 0
\]
- Second factor:
\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]

Thus, the solutions to the equation \(12x^2 = 36x\) are:
\[
x = 0 \quad \text{and} \quad x = 3
\]

In conclusion, the standard form of the quadratic equation is:
\[
12x^2 - 36x = 0
\]
and the solutions are \(x = 0\) and \(x = 3\).