check the solution of 2x²/4-x/6=3/2?
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Answer:
x = (1 + √109)/6 and x = (1 - √109)/6
Step-by-step explanation:
Rational Algebraic Equation:
2x²/4 - x/6 = 3/2
Multiply each term by their LCD 12:
(12) [2x²/4 - x/6 = 3/2] (12)
6x² - 2x = 18
6x² - 2x - 18 = 0
2(3x² - x - 9) = 0
Complete the square:
3x²-x = 9
x² - x + [(-1/3)(1/2)]² = 9/3 + [(-1/3)(1/2)]²
x² - x + (1/6)² = 3 + (1/6)²
(x - 1/6)² = 3 + (1/36)
(x - 1/6)² = (108/36) + (1/36)
(x - 1/6)² = (109/36)
√(x - 1/6)² = ± √(109/36)
x - 1/6 = ± (√109)/6
x = 1/6 ± √109)/6
x = (1 + √109)/6 and x = (1 - √109)/6