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Simplifying (6x + 8) = (3x2 + -6x + -5) Reorder the terms: (8 + 6x) = (3x2 + -6x + -5) Remove parenthesis around (8 + 6x) 8 + 6x = (3x2 + -6x + -5) Reorder the terms: 8 + 6x = (-5 + -6x + 3x2) Remove parenthesis around (-5 + -6x + 3x2) 8 + 6x = -5 + -6x + 3x2 Solving 8 + 6x = -5 + -6x + 3x2 Solving for variable 'x'. Reorder the terms: 8 + 5 + 6x + 6x + -3x2 = -5 + -6x + 3x2 + 5 + 6x + -3x2 Combine like terms: 8 + 5 = 13 13 + 6x + 6x + -3x2 = -5 + -6x + 3x2 + 5 + 6x + -3x2 Combine like terms: 6x + 6x = 12x 13 + 12x + -3x2 = -5 + -6x + 3x2 + 5 + 6x + -3x2 Reorder the terms: 13 + 12x + -3x2 = -5 + 5 + -6x + 6x + 3x2 + -3x2 Combine like terms: -5 + 5 = 0 13 + 12x + -3x2 = 0 + -6x + 6x + 3x2 + -3x2 13 + 12x + -3x2 = -6x + 6x + 3x2 + -3x2 Combine like terms: -6x + 6x = 0 13 + 12x + -3x2 = 0 + 3x2 + -3x2 13 + 12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 13 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4.333333333 + -4x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -4x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -4x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -4x + x2 = 0 + 4.333333333 -4x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -4x + x2 = 4.333333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4.333333333 + 4 Reorder the terms: 4 + -4x + x2 = 4.333333333 + 4 Combine like terms: 4.333333333 + 4 = 8.333333333 4 + -4x + x2 = 8.333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 8.333333333 Calculate the square root of the right side: 2.886751346 Break this problem into two subproblems by setting (x + -2) equal to 2.886751346 and -2.886751346.Subproblem 1
x + -2 = 2.886751346 Simplifying x + -2 = 2.886751346 Reorder the terms: -2 + x = 2.886751346 Solving -2 + x = 2.886751346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.886751346 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.886751346 + 2 x = 2.886751346 + 2 Combine like terms: 2.886751346 + 2 = 4.886751346 x = 4.886751346 Simplifying x = 4.886751346Subproblem 2
x + -2 = -2.886751346 Simplifying x + -2 = -2.886751346 Reorder the terms: -2 + x = -2.886751346 Solving -2 + x = -2.886751346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.886751346 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.886751346 + 2 x = -2.886751346 + 2 Combine like terms: -2.886751346 + 2 = -0.886751346 x = -0.886751346 Simplifying x = -0.886751346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.886751346, -0.886751346}
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