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Simplifying (x + 10)(x + 12) = 240 Reorder the terms: (10 + x)(x + 12) = 240 Reorder the terms: (10 + x)(12 + x) = 240 Multiply (10 + x) * (12 + x) (10(12 + x) + x(12 + x)) = 240 ((12 * 10 + x * 10) + x(12 + x)) = 240 ((120 + 10x) + x(12 + x)) = 240 (120 + 10x + (12 * x + x * x)) = 240 (120 + 10x + (12x + x2)) = 240 Combine like terms: 10x + 12x = 22x (120 + 22x + x2) = 240 Solving 120 + 22x + x2 = 240 Solving for variable 'x'. Reorder the terms: 120 + -240 + 22x + x2 = 240 + -240 Combine like terms: 120 + -240 = -120 -120 + 22x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -120 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 22x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 22x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 22x + x2 = 0 + 120 22x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 22x + x2 = 120 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 120 + 121 Reorder the terms: 121 + 22x + x2 = 120 + 121 Combine like terms: 120 + 121 = 241 121 + 22x + x2 = 241 Factor a perfect square on the left side: (x + 11)(x + 11) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + 11) equal to 15.524174696 and -15.524174696.Subproblem 1
x + 11 = 15.524174696 Simplifying x + 11 = 15.524174696 Reorder the terms: 11 + x = 15.524174696 Solving 11 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 15.524174696 + -11 Combine like terms: 11 + -11 = 0 0 + x = 15.524174696 + -11 x = 15.524174696 + -11 Combine like terms: 15.524174696 + -11 = 4.524174696 x = 4.524174696 Simplifying x = 4.524174696Subproblem 2
x + 11 = -15.524174696 Simplifying x + 11 = -15.524174696 Reorder the terms: 11 + x = -15.524174696 Solving 11 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -15.524174696 + -11 Combine like terms: 11 + -11 = 0 0 + x = -15.524174696 + -11 x = -15.524174696 + -11 Combine like terms: -15.524174696 + -11 = -26.524174696 x = -26.524174696 Simplifying x = -26.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.524174696, -26.524174696}
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