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Simplifying 2x2 + 10x + -100 = x2 + 9x + 60 Reorder the terms: -100 + 10x + 2x2 = x2 + 9x + 60 Reorder the terms: -100 + 10x + 2x2 = 60 + 9x + x2 Solving -100 + 10x + 2x2 = 60 + 9x + x2 Solving for variable 'x'. Reorder the terms: -100 + -60 + 10x + -9x + 2x2 + -1x2 = 60 + 9x + x2 + -60 + -9x + -1x2 Combine like terms: -100 + -60 = -160 -160 + 10x + -9x + 2x2 + -1x2 = 60 + 9x + x2 + -60 + -9x + -1x2 Combine like terms: 10x + -9x = 1x -160 + 1x + 2x2 + -1x2 = 60 + 9x + x2 + -60 + -9x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -160 + 1x + 1x2 = 60 + 9x + x2 + -60 + -9x + -1x2 Reorder the terms: -160 + 1x + 1x2 = 60 + -60 + 9x + -9x + x2 + -1x2 Combine like terms: 60 + -60 = 0 -160 + 1x + 1x2 = 0 + 9x + -9x + x2 + -1x2 -160 + 1x + 1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 -160 + 1x + 1x2 = 0 + x2 + -1x2 -160 + 1x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -160 + 1x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 1x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 1x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 1x + x2 = 0 + 160 1x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 1x + x2 = 160 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 160 + 0.25 Reorder the terms: 0.25 + x + x2 = 160 + 0.25 Combine like terms: 160 + 0.25 = 160.25 0.25 + x + x2 = 160.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (x + 0.5) equal to 12.658988901 and -12.658988901.Subproblem 1
x + 0.5 = 12.658988901 Simplifying x + 0.5 = 12.658988901 Reorder the terms: 0.5 + x = 12.658988901 Solving 0.5 + x = 12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 12.658988901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.658988901 + -0.5 x = 12.658988901 + -0.5 Combine like terms: 12.658988901 + -0.5 = 12.158988901 x = 12.158988901 Simplifying x = 12.158988901Subproblem 2
x + 0.5 = -12.658988901 Simplifying x + 0.5 = -12.658988901 Reorder the terms: 0.5 + x = -12.658988901 Solving 0.5 + x = -12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -12.658988901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.658988901 + -0.5 x = -12.658988901 + -0.5 Combine like terms: -12.658988901 + -0.5 = -13.158988901 x = -13.158988901 Simplifying x = -13.158988901Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.158988901, -13.158988901}
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