Solve the quadratic equation 2x2+4x=−12 . Which of the following expresses its solutions in the form a±bi ?
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Solve 2x^2 + 4x = −12. Move −12 to the left: 2x^2 + 4x + 12 = 0. Divide by 2: x^2 + 2x + 6 = 0.
Use the quadratic formula: x = [−2 ± sqrt(2^2 − 4·1·6)]/2 = [−2 ± sqrt(4 − 24)]/2 = [−2 ± sqrt(−20)]/2
= [−2 ± 2i√5]/2 = −1 ± i√5.
So the solutions are x = −1 ± i√5 (a = −1, b = √5).
Use the quadratic formula: x = [−2 ± sqrt(2^2 − 4·1·6)]/2 = [−2 ± sqrt(4 − 24)]/2 = [−2 ± sqrt(−20)]/2
= [−2 ± 2i√5]/2 = −1 ± i√5.
So the solutions are x = −1 ± i√5 (a = −1, b = √5).
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