3x^2+4x-6=0

Question

complete the square

Answer 1

3x² + 4x - 6 = 0               Given

(3x² + 4x - 6)/3 = 0         Divide both sides by 3 (the coefficient of x²)

x² + (4/3)x - 2 = 0           Divide each term by 3 (distributing)

x² + (4/3)x = 2                Add 2 to each side

                                         [(4/3)/2]² = [2/3]² = 4/9   Find the "(a/2b)²" term

x² + (4/3)x + 4/9 = 2 + 4/9  Add 4/9 to each side

(x + 2/3)² = 2 + 4/9          Factor the left side into the perfect square

(x + 2/3)² = 18/9 + 4/9      Find the common denominator for the right side

(x + 2/3)² = 22/9                Simplify

x + 2/3 = +/- √(22/9)         Take the square root of both sides

x + 2/3 = +/- √(22)/3         Simplify

x = -2/3 +/- √(22)/3          Subtract 2/3 from each side

x = (-2 +/- √(22))/3          Combine terms over the common denominator