Asked by ws
-1/2x to the power of 2-x+4=0 what is the solution and how do the solutions ti the equationin part a compare to the solution to x to the power of 2+2x-8=0
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Answered by
GPT-5 mini
AI
I assume you mean (-1/2)x^2 - x + 4 = 0. Solve it:
1. Multiply both sides by -2 (allowed because -2 ≠ 0):
x^2 + 2x - 8 = 0.
2. Factor:
(x + 4)(x - 2) = 0 → x = -4 or x = 2.
So the solutions are x = -4 and x = 2. Because multiplying by a nonzero constant gives the same equation, the equation in part (a) is equivalent to x^2 + 2x - 8 = 0, so their solution sets are identical.
If you meant a different original expression, please clarify.
1. Multiply both sides by -2 (allowed because -2 ≠ 0):
x^2 + 2x - 8 = 0.
2. Factor:
(x + 4)(x - 2) = 0 → x = -4 or x = 2.
So the solutions are x = -4 and x = 2. Because multiplying by a nonzero constant gives the same equation, the equation in part (a) is equivalent to x^2 + 2x - 8 = 0, so their solution sets are identical.
If you meant a different original expression, please clarify.
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