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Which equation is equivalent to the given equation?

Given: [tex]-126 = 2x^2 - 32x[/tex]

A. [tex]2x^2 + 32x - 126 = 0[/tex]

B. [tex]2x^2 - 32x - 126 = 0[/tex]

C. [tex]2x^2 + 32x + 126 = 0[/tex]

D. [tex]2x^2 - 32x + 126 = 0[/tex]

Answer :

To find an equation equivalent to the given equation, [tex]\(-126 = 2x^2 - 32x\)[/tex], we need to transform it into a standard quadratic equation form, which is [tex]\(ax^2 + bx + c = 0\)[/tex].

Here's how we do it:

1. Start with the given equation:
[tex]\[
-126 = 2x^2 - 32x
\][/tex]

2. To move all the terms to one side of the equation, add 126 to both sides:
[tex]\[
0 = 2x^2 - 32x + 126
\][/tex]

3. This gives us the equation in the standard quadratic form:
[tex]\[
2x^2 - 32x + 126 = 0
\][/tex]

Now let's compare this with the options provided:

- [tex]\(2x^2 + 32x - 126 = 0\)[/tex]
- [tex]\(2x^2 - 32x - 126 = 0\)[/tex]
- [tex]\(2x^2 + 32x + 126 = 0\)[/tex]
- [tex]\(2x^2 - 32x + 126 = 0\)[/tex]

The equation [tex]\(2x^2 - 32x + 126 = 0\)[/tex] matches our transformed version, so this is the equation equivalent to the given one.

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