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Answer :
To solve the equation [tex]\(2x^2 - 126 = -4x\)[/tex] and find an equivalent equation, we need to rearrange it so that one side equals zero. Here's a step-by-step guide on how to do this:
1. Start with the given equation:
[tex]\[
2x^2 - 126 = -4x
\][/tex]
2. Move all terms to one side to set the equation to zero:
- Add [tex]\(4x\)[/tex] to both sides of the equation to move the [tex]\(-4x\)[/tex] term.
[tex]\[
2x^2 - 126 + 4x = 0
\][/tex]
3. Rearrange the terms, if necessary, to write them in standard form:
- The standard form for quadratics is [tex]\(ax^2 + bx + c = 0\)[/tex].
- Writing the terms in order of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and then the constant gives:
[tex]\[
2x^2 + 4x - 126 = 0
\][/tex]
By completing these steps, we find that the equation equivalent to the original is:
[tex]\[
2x^2 + 4x - 126 = 0
\][/tex]
This rearranged equation is the correct and equivalent form of the given equation.
1. Start with the given equation:
[tex]\[
2x^2 - 126 = -4x
\][/tex]
2. Move all terms to one side to set the equation to zero:
- Add [tex]\(4x\)[/tex] to both sides of the equation to move the [tex]\(-4x\)[/tex] term.
[tex]\[
2x^2 - 126 + 4x = 0
\][/tex]
3. Rearrange the terms, if necessary, to write them in standard form:
- The standard form for quadratics is [tex]\(ax^2 + bx + c = 0\)[/tex].
- Writing the terms in order of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and then the constant gives:
[tex]\[
2x^2 + 4x - 126 = 0
\][/tex]
By completing these steps, we find that the equation equivalent to the original is:
[tex]\[
2x^2 + 4x - 126 = 0
\][/tex]
This rearranged equation is the correct and equivalent form of the given equation.
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