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Simplifying 11(4 + -6x + 5)(13x + 1) = 5 Reorder the terms: 11(4 + 5 + -6x)(13x + 1) = 5 Combine like terms: 4 + 5 = 9 11(9 + -6x)(13x + 1) = 5 Reorder the terms: 11(9 + -6x)(1 + 13x) = 5 Multiply (9 + -6x) * (1 + 13x) 11(9(1 + 13x) + -6x * (1 + 13x)) = 5 11((1 * 9 + 13x * 9) + -6x * (1 + 13x)) = 5 11((9 + 117x) + -6x * (1 + 13x)) = 5 11(9 + 117x + (1 * -6x + 13x * -6x)) = 5 11(9 + 117x + (-6x + -78x2)) = 5 Combine like terms: 117x + -6x = 111x 11(9 + 111x + -78x2) = 5 (9 * 11 + 111x * 11 + -78x2 * 11) = 5 (99 + 1221x + -858x2) = 5 Solving 99 + 1221x + -858x2 = 5 Solving for variable 'x'. Reorder the terms: 99 + -5 + 1221x + -858x2 = 5 + -5 Combine like terms: 99 + -5 = 94 94 + 1221x + -858x2 = 5 + -5 Combine like terms: 5 + -5 = 0 94 + 1221x + -858x2 = 0 Begin completing the square. Divide all terms by -858 the coefficient of the squared term: Divide each side by '-858'. -0.1095571096 + -1.423076923x + x2 = 0 Move the constant term to the right: Add '0.1095571096' to each side of the equation. -0.1095571096 + -1.423076923x + 0.1095571096 + x2 = 0 + 0.1095571096 Reorder the terms: -0.1095571096 + 0.1095571096 + -1.423076923x + x2 = 0 + 0.1095571096 Combine like terms: -0.1095571096 + 0.1095571096 = 0.0000000000 0.0000000000 + -1.423076923x + x2 = 0 + 0.1095571096 -1.423076923x + x2 = 0 + 0.1095571096 Combine like terms: 0 + 0.1095571096 = 0.1095571096 -1.423076923x + x2 = 0.1095571096 The x term is -1.423076923x. Take half its coefficient (-0.7115384615). Square it (0.5062869822) and add it to both sides. Add '0.5062869822' to each side of the equation. -1.423076923x + 0.5062869822 + x2 = 0.1095571096 + 0.5062869822 Reorder the terms: 0.5062869822 + -1.423076923x + x2 = 0.1095571096 + 0.5062869822 Combine like terms: 0.1095571096 + 0.5062869822 = 0.6158440918 0.5062869822 + -1.423076923x + x2 = 0.6158440918 Factor a perfect square on the left side: (x + -0.7115384615)(x + -0.7115384615) = 0.6158440918 Calculate the square root of the right side: 0.784757346 Break this problem into two subproblems by setting (x + -0.7115384615) equal to 0.784757346 and -0.784757346.Subproblem 1
x + -0.7115384615 = 0.784757346 Simplifying x + -0.7115384615 = 0.784757346 Reorder the terms: -0.7115384615 + x = 0.784757346 Solving -0.7115384615 + x = 0.784757346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7115384615' to each side of the equation. -0.7115384615 + 0.7115384615 + x = 0.784757346 + 0.7115384615 Combine like terms: -0.7115384615 + 0.7115384615 = 0.0000000000 0.0000000000 + x = 0.784757346 + 0.7115384615 x = 0.784757346 + 0.7115384615 Combine like terms: 0.784757346 + 0.7115384615 = 1.4962958075 x = 1.4962958075 Simplifying x = 1.4962958075Subproblem 2
x + -0.7115384615 = -0.784757346 Simplifying x + -0.7115384615 = -0.784757346 Reorder the terms: -0.7115384615 + x = -0.784757346 Solving -0.7115384615 + x = -0.784757346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7115384615' to each side of the equation. -0.7115384615 + 0.7115384615 + x = -0.784757346 + 0.7115384615 Combine like terms: -0.7115384615 + 0.7115384615 = 0.0000000000 0.0000000000 + x = -0.784757346 + 0.7115384615 x = -0.784757346 + 0.7115384615 Combine like terms: -0.784757346 + 0.7115384615 = -0.0732188845 x = -0.0732188845 Simplifying x = -0.0732188845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4962958075, -0.0732188845}
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