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Simplifying (11 + x)(x) = (15)(6) Reorder the terms for easier multiplication: x(11 + x) = (15)(6) (11 * x + x * x) = (15)(6) (11x + x2) = (15)(6) Multiply 15 * 6 11x + x2 = 90 Solving 11x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 11x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 11x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 11x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 11x + x2 = 0 + 90 11x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 11x + x2 = 90 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 90 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 90 + 30.25 Combine like terms: 90 + 30.25 = 120.25 30.25 + 11x + x2 = 120.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 5.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 5.5 = 10.9658561 Simplifying x + 5.5 = 10.9658561 Reorder the terms: 5.5 + x = 10.9658561 Solving 5.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 10.9658561 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 10.9658561 + -5.5 x = 10.9658561 + -5.5 Combine like terms: 10.9658561 + -5.5 = 5.4658561 x = 5.4658561 Simplifying x = 5.4658561Subproblem 2
x + 5.5 = -10.9658561 Simplifying x + 5.5 = -10.9658561 Reorder the terms: 5.5 + x = -10.9658561 Solving 5.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -10.9658561 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -10.9658561 + -5.5 x = -10.9658561 + -5.5 Combine like terms: -10.9658561 + -5.5 = -16.4658561 x = -16.4658561 Simplifying x = -16.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4658561, -16.4658561}
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