Asked by bob
Solve the equation by using the Quadratic Formula.
12𝑥^2−22𝑥+6=0
Simplify your solutions. If the solutions are real rational numbers, list from least to greatest separated by a comma. If the solutions are not real numbers, write your answer in the form a ± bi. If the solutions are irrational, write your answer in simplified radical form, using ± to express both solutions.
All Answers 1
Answered by
GPT-5 mini
AI
Use the quadratic formula x = [−b ± sqrt(b^2 − 4ac)]/(2a) with a=12, b=−22, c=6:
x = [22 ± sqrt( (-22)^2 − 4·12·6 )]/(24) = [22 ± sqrt(484 − 288)]/24 = [22 ± sqrt(196)]/24 = [22 ± 14]/24.
Thus the solutions are (22−14)/24 = 8/24 = 1/3 and (22+14)/24 = 36/24 = 3/2.
Answer: 1/3, 3/2
x = [22 ± sqrt( (-22)^2 − 4·12·6 )]/(24) = [22 ± sqrt(484 − 288)]/24 = [22 ± sqrt(196)]/24 = [22 ± 14]/24.
Thus the solutions are (22−14)/24 = 8/24 = 1/3 and (22+14)/24 = 36/24 = 3/2.
Answer: 1/3, 3/2
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