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Simplifying x2 + -25x + -125 = 0 Reorder the terms: -125 + -25x + x2 = 0 Solving -125 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -25x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -25x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -25x + x2 = 0 + 125 -25x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -25x + x2 = 125 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 = 125 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 125 + 156.25 Combine like terms: 125 + 156.25 = 281.25 156.25 + -25x + x2 = 281.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 281.25 Calculate the square root of the right side: 16.770509831 Break this problem into two subproblems by setting (x + -12.5) equal to 16.770509831 and -16.770509831.Subproblem 1
x + -12.5 = 16.770509831 Simplifying x + -12.5 = 16.770509831 Reorder the terms: -12.5 + x = 16.770509831 Solving -12.5 + x = 16.770509831 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 = 16.770509831 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 16.770509831 + 12.5 x = 16.770509831 + 12.5 Combine like terms: 16.770509831 + 12.5 = 29.270509831 x = 29.270509831 Simplifying x = 29.270509831Subproblem 2
x + -12.5 = -16.770509831 Simplifying x + -12.5 = -16.770509831 Reorder the terms: -12.5 + x = -16.770509831 Solving -12.5 + x = -16.770509831 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 = -16.770509831 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -16.770509831 + 12.5 x = -16.770509831 + 12.5 Combine like terms: -16.770509831 + 12.5 = -4.270509831 x = -4.270509831 Simplifying x = -4.270509831Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.270509831, -4.270509831}
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