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Simplifying (9 + -1x)(12 + -1x) = 50 Multiply (9 + -1x) * (12 + -1x) (9(12 + -1x) + -1x * (12 + -1x)) = 50 ((12 * 9 + -1x * 9) + -1x * (12 + -1x)) = 50 ((108 + -9x) + -1x * (12 + -1x)) = 50 (108 + -9x + (12 * -1x + -1x * -1x)) = 50 (108 + -9x + (-12x + 1x2)) = 50 Combine like terms: -9x + -12x = -21x (108 + -21x + 1x2) = 50 Solving 108 + -21x + 1x2 = 50 Solving for variable 'x'. Reorder the terms: 108 + -50 + -21x + 1x2 = 50 + -50 Combine like terms: 108 + -50 = 58 58 + -21x + 1x2 = 50 + -50 Combine like terms: 50 + -50 = 0 58 + -21x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + -21x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + -21x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -21x + x2 = 0 + -58 -21x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 -21x + x2 = -58 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -58 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -58 + 110.25 Combine like terms: -58 + 110.25 = 52.25 110.25 + -21x + x2 = 52.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -10.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + -10.5 = 7.228416147 Simplifying x + -10.5 = 7.228416147 Reorder the terms: -10.5 + x = 7.228416147 Solving -10.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 7.228416147 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 7.228416147 + 10.5 x = 7.228416147 + 10.5 Combine like terms: 7.228416147 + 10.5 = 17.728416147 x = 17.728416147 Simplifying x = 17.728416147Subproblem 2
x + -10.5 = -7.228416147 Simplifying x + -10.5 = -7.228416147 Reorder the terms: -10.5 + x = -7.228416147 Solving -10.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -7.228416147 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -7.228416147 + 10.5 x = -7.228416147 + 10.5 Combine like terms: -7.228416147 + 10.5 = 3.271583853 x = 3.271583853 Simplifying x = 3.271583853Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.728416147, 3.271583853}
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