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Simplifying (7 + -1x)(12 + -1x) = 83 + -31.5 Multiply (7 + -1x) * (12 + -1x) (7(12 + -1x) + -1x * (12 + -1x)) = 83 + -31.5 ((12 * 7 + -1x * 7) + -1x * (12 + -1x)) = 83 + -31.5 ((84 + -7x) + -1x * (12 + -1x)) = 83 + -31.5 (84 + -7x + (12 * -1x + -1x * -1x)) = 83 + -31.5 (84 + -7x + (-12x + 1x2)) = 83 + -31.5 Combine like terms: -7x + -12x = -19x (84 + -19x + 1x2) = 83 + -31.5 Combine like terms: 83 + -31.5 = 51.5 84 + -19x + 1x2 = 51.5 Solving 84 + -19x + 1x2 = 51.5 Solving for variable 'x'. Reorder the terms: 84 + -51.5 + -19x + 1x2 = 51.5 + -51.5 Combine like terms: 84 + -51.5 = 32.5 32.5 + -19x + 1x2 = 51.5 + -51.5 Combine like terms: 51.5 + -51.5 = 0.0 32.5 + -19x + 1x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-32.5' to each side of the equation. 32.5 + -19x + -32.5 + x2 = 0.0 + -32.5 Reorder the terms: 32.5 + -32.5 + -19x + x2 = 0.0 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + -19x + x2 = 0.0 + -32.5 -19x + x2 = 0.0 + -32.5 Combine like terms: 0.0 + -32.5 = -32.5 -19x + x2 = -32.5 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -32.5 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -32.5 + 90.25 Combine like terms: -32.5 + 90.25 = 57.75 90.25 + -19x + x2 = 57.75 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 57.75 Calculate the square root of the right side: 7.599342077 Break this problem into two subproblems by setting (x + -9.5) equal to 7.599342077 and -7.599342077.Subproblem 1
x + -9.5 = 7.599342077 Simplifying x + -9.5 = 7.599342077 Reorder the terms: -9.5 + x = 7.599342077 Solving -9.5 + x = 7.599342077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 7.599342077 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 7.599342077 + 9.5 x = 7.599342077 + 9.5 Combine like terms: 7.599342077 + 9.5 = 17.099342077 x = 17.099342077 Simplifying x = 17.099342077Subproblem 2
x + -9.5 = -7.599342077 Simplifying x + -9.5 = -7.599342077 Reorder the terms: -9.5 + x = -7.599342077 Solving -9.5 + x = -7.599342077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -7.599342077 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -7.599342077 + 9.5 x = -7.599342077 + 9.5 Combine like terms: -7.599342077 + 9.5 = 1.900657923 x = 1.900657923 Simplifying x = 1.900657923Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.099342077, 1.900657923}
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