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Simplifying (6 + -1x)(6 + x) + -1(x + -11) * x = 18 Multiply (6 + -1x) * (6 + x) (6(6 + x) + -1x * (6 + x)) + -1(x + -11) * x = 18 ((6 * 6 + x * 6) + -1x * (6 + x)) + -1(x + -11) * x = 18 ((36 + 6x) + -1x * (6 + x)) + -1(x + -11) * x = 18 (36 + 6x + (6 * -1x + x * -1x)) + -1(x + -11) * x = 18 (36 + 6x + (-6x + -1x2)) + -1(x + -11) * x = 18 Combine like terms: 6x + -6x = 0 (36 + 0 + -1x2) + -1(x + -11) * x = 18 (36 + -1x2) + -1(x + -11) * x = 18 Reorder the terms: 36 + -1x2 + -1(-11 + x) * x = 18 Reorder the terms for easier multiplication: 36 + -1x2 + -1x(-11 + x) = 18 36 + -1x2 + (-11 * -1x + x * -1x) = 18 36 + -1x2 + (11x + -1x2) = 18 Reorder the terms: 36 + 11x + -1x2 + -1x2 = 18 Combine like terms: -1x2 + -1x2 = -2x2 36 + 11x + -2x2 = 18 Solving 36 + 11x + -2x2 = 18 Solving for variable 'x'. Reorder the terms: 36 + -18 + 11x + -2x2 = 18 + -18 Combine like terms: 36 + -18 = 18 18 + 11x + -2x2 = 18 + -18 Combine like terms: 18 + -18 = 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 = 6.819705149 x = 6.819705149 Simplifying x = 6.819705149Subproblem 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 = -1.319705149 x = -1.319705149 Simplifying x = -1.319705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.819705149, -1.319705149}
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