Answer :
To find an equation equivalent to [tex]\(-27 = -3x^2 + 24x\)[/tex], we need to rearrange it into a standard form, which typically is [tex]\(ax^2 + bx + c = 0\)[/tex].
Here’s a step-by-step solution:
1. Start with the given equation:
[tex]\(-27 = -3x^2 + 24x\)[/tex].
2. Move all terms to one side of the equation so that the equation equals zero. This is done by adding [tex]\(3x^2\)[/tex] and subtracting [tex]\(24x\)[/tex] from both sides:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
Here’s how it looks when equalizing it to zero:
- Add [tex]\(3x^2\)[/tex] to both sides:
[tex]\[
3x^2 - 27 = 24x
\][/tex]
- Subtract [tex]\(24x\)[/tex] from both sides:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
3. Final equivalent equation:
[tex]\(3x^2 - 24x - 27 = 0\)[/tex].
Thus, the equation equivalent to [tex]\(-27 = -3x^2 + 24x\)[/tex] is:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
Therefore, the correct answer is:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
Here’s a step-by-step solution:
1. Start with the given equation:
[tex]\(-27 = -3x^2 + 24x\)[/tex].
2. Move all terms to one side of the equation so that the equation equals zero. This is done by adding [tex]\(3x^2\)[/tex] and subtracting [tex]\(24x\)[/tex] from both sides:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
Here’s how it looks when equalizing it to zero:
- Add [tex]\(3x^2\)[/tex] to both sides:
[tex]\[
3x^2 - 27 = 24x
\][/tex]
- Subtract [tex]\(24x\)[/tex] from both sides:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
3. Final equivalent equation:
[tex]\(3x^2 - 24x - 27 = 0\)[/tex].
Thus, the equation equivalent to [tex]\(-27 = -3x^2 + 24x\)[/tex] is:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
Therefore, the correct answer is:
[tex]\[
3x^2 - 24x - 27 = 0
\][/tex]
