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Answer :
We start with the equation
[tex]$$-2x^2 + 32x = 126.$$[/tex]
Step 1. Bring all terms to one side of the equation
Subtract [tex]\(126\)[/tex] from both sides to obtain
[tex]$$-2x^2 + 32x - 126 = 0.$$[/tex]
Step 2. Multiply both sides by [tex]\(-1\)[/tex]
Multiplying the entire equation by [tex]\(-1\)[/tex] (which maintains the equality) gives
[tex]$$2x^2 - 32x + 126 = 0.$$[/tex]
Step 3. Compare with the available options
The equation we obtained is
[tex]$$2x^2 - 32x + 126 = 0.$$[/tex]
Among the given options:
1) [tex]\(2x^2 + 32x + 126 = 0\)[/tex]
2) [tex]\(2x^2 - 32x - 126 = 0\)[/tex]
3) [tex]\(2x^2 + 32x - 126 = 0\)[/tex]
4) [tex]\(2x^2 - 32x + 126 = 0\)[/tex]
We see that option 4 exactly matches the equation we derived.
Final Answer: Option 4:
[tex]$$2x^2 - 32x + 126 = 0.$$[/tex]
[tex]$$-2x^2 + 32x = 126.$$[/tex]
Step 1. Bring all terms to one side of the equation
Subtract [tex]\(126\)[/tex] from both sides to obtain
[tex]$$-2x^2 + 32x - 126 = 0.$$[/tex]
Step 2. Multiply both sides by [tex]\(-1\)[/tex]
Multiplying the entire equation by [tex]\(-1\)[/tex] (which maintains the equality) gives
[tex]$$2x^2 - 32x + 126 = 0.$$[/tex]
Step 3. Compare with the available options
The equation we obtained is
[tex]$$2x^2 - 32x + 126 = 0.$$[/tex]
Among the given options:
1) [tex]\(2x^2 + 32x + 126 = 0\)[/tex]
2) [tex]\(2x^2 - 32x - 126 = 0\)[/tex]
3) [tex]\(2x^2 + 32x - 126 = 0\)[/tex]
4) [tex]\(2x^2 - 32x + 126 = 0\)[/tex]
We see that option 4 exactly matches the equation we derived.
Final Answer: Option 4:
[tex]$$2x^2 - 32x + 126 = 0.$$[/tex]
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