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Simplifying 12 = (x + 6)(2x + -1) Reorder the terms: 12 = (6 + x)(2x + -1) Reorder the terms: 12 = (6 + x)(-1 + 2x) Multiply (6 + x) * (-1 + 2x) 12 = (6(-1 + 2x) + x(-1 + 2x)) 12 = ((-1 * 6 + 2x * 6) + x(-1 + 2x)) 12 = ((-6 + 12x) + x(-1 + 2x)) 12 = (-6 + 12x + (-1 * x + 2x * x)) 12 = (-6 + 12x + (-1x + 2x2)) Combine like terms: 12x + -1x = 11x 12 = (-6 + 11x + 2x2) Solving 12 = -6 + 11x + 2x2 Solving for variable 'x'. Combine like terms: 12 + 6 = 18 18 + -11x + -2x2 = -6 + 11x + 2x2 + 6 + -11x + -2x2 Reorder the terms: 18 + -11x + -2x2 = -6 + 6 + 11x + -11x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 18 + -11x + -2x2 = 0 + 11x + -11x + 2x2 + -2x2 18 + -11x + -2x2 = 11x + -11x + 2x2 + -2x2 Combine like terms: 11x + -11x = 0 18 + -11x + -2x2 = 0 + 2x2 + -2x2 18 + -11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 18 + -11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -9 + 5.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 5.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 5.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5.5x + x2 = 0 + 9 5.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 5.5x + x2 = 9 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 9 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 9 + 7.5625 Combine like terms: 9 + 7.5625 = 16.5625 7.5625 + 5.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + 2.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + 2.75 = 4.069705149 Simplifying x + 2.75 = 4.069705149 Reorder the terms: 2.75 + x = 4.069705149 Solving 2.75 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.069705149 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.069705149 + -2.75 x = 4.069705149 + -2.75 Combine like terms: 4.069705149 + -2.75 = 1.319705149 x = 1.319705149 Simplifying x = 1.319705149Subproblem 2
x + 2.75 = -4.069705149 Simplifying x + 2.75 = -4.069705149 Reorder the terms: 2.75 + x = -4.069705149 Solving 2.75 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.069705149 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.069705149 + -2.75 x = -4.069705149 + -2.75 Combine like terms: -4.069705149 + -2.75 = -6.819705149 x = -6.819705149 Simplifying x = -6.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.319705149, -6.819705149}
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