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Simplifying (8 + -1x)(17 + -1x) = 66 Multiply (8 + -1x) * (17 + -1x) (8(17 + -1x) + -1x * (17 + -1x)) = 66 ((17 * 8 + -1x * 8) + -1x * (17 + -1x)) = 66 ((136 + -8x) + -1x * (17 + -1x)) = 66 (136 + -8x + (17 * -1x + -1x * -1x)) = 66 (136 + -8x + (-17x + 1x2)) = 66 Combine like terms: -8x + -17x = -25x (136 + -25x + 1x2) = 66 Solving 136 + -25x + 1x2 = 66 Solving for variable 'x'. Reorder the terms: 136 + -66 + -25x + 1x2 = 66 + -66 Combine like terms: 136 + -66 = 70 70 + -25x + 1x2 = 66 + -66 Combine like terms: 66 + -66 = 0 70 + -25x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -25x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -25x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -25x + x2 = 0 + -70 -25x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -25x + x2 = -70 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -70 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -70 + 156.25 Combine like terms: -70 + 156.25 = 86.25 156.25 + -25x + x2 = 86.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -12.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -12.5 = 9.287087811 Simplifying x + -12.5 = 9.287087811 Reorder the terms: -12.5 + x = 9.287087811 Solving -12.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 9.287087811 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 9.287087811 + 12.5 x = 9.287087811 + 12.5 Combine like terms: 9.287087811 + 12.5 = 21.787087811 x = 21.787087811 Simplifying x = 21.787087811Subproblem 2
x + -12.5 = -9.287087811 Simplifying x + -12.5 = -9.287087811 Reorder the terms: -12.5 + x = -9.287087811 Solving -12.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -9.287087811 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -9.287087811 + 12.5 x = -9.287087811 + 12.5 Combine like terms: -9.287087811 + 12.5 = 3.212912189 x = 3.212912189 Simplifying x = 3.212912189Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.787087811, 3.212912189}
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