Complete the square

2x^2+3x-2

Correct answer: (2 x - 1) (x + 2)

Step-by-step explanation:

Given:

2 x² + 3 x - 2 = () · ()

2 x² + 3 x - 2 = 2 · (x² + (3/2) x - 1) = 2 (x² + 2 · x · (3/4) + (3/4) ² - (3/4) ² - 1)

2 x² + 3 x - 2 = 2 · ((x + (3/4)) ² - (9/16) - 1) = 2 · ((x + (3/4)) ² - (9/16) - (16/16))

2 x² + 3 x - 2 = 2 · ((x + (3/4)) ² - (25/16)) = 2 · ((x + (3/4)) ² - (5/4) ²)

2 x² + 3 x - 2 = 2 · (x + (3/4) - (5/4)) · (x + (3/4) + (5/4)) =

2 · (x - (2/4)) (x + (8/4))

2 x² + 3 x - 2 = 2 · (x - (1/2)) (x + 2) = (2 x - 1) · (x + 2)

2 x² + 3 x - 2 = (2 x - 1) · (x + 2)

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