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Simplifying x(x + -0.10) = 60 Reorder the terms: x(-0.10 + x) = 60 (-0.10 * x + x * x) = 60 (-0.10x + x2) = 60 Solving -0.10x + x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + -0.10x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -0.10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -0.10x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -0.10x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -0.10x + x2 = 0 + 60 -0.10x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -0.10x + x2 = 60 The x term is -0.10x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.10x + 0.0025 + x2 = 60 + 0.0025 Reorder the terms: 0.0025 + -0.10x + x2 = 60 + 0.0025 Combine like terms: 60 + 0.0025 = 60.0025 0.0025 + -0.10x + x2 = 60.0025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 60.0025 Calculate the square root of the right side: 7.746128065 Break this problem into two subproblems by setting (x + -0.05) equal to 7.746128065 and -7.746128065.Subproblem 1
x + -0.05 = 7.746128065 Simplifying x + -0.05 = 7.746128065 Reorder the terms: -0.05 + x = 7.746128065 Solving -0.05 + x = 7.746128065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 7.746128065 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 7.746128065 + 0.05 x = 7.746128065 + 0.05 Combine like terms: 7.746128065 + 0.05 = 7.796128065 x = 7.796128065 Simplifying x = 7.796128065Subproblem 2
x + -0.05 = -7.746128065 Simplifying x + -0.05 = -7.746128065 Reorder the terms: -0.05 + x = -7.746128065 Solving -0.05 + x = -7.746128065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -7.746128065 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -7.746128065 + 0.05 x = -7.746128065 + 0.05 Combine like terms: -7.746128065 + 0.05 = -7.696128065 x = -7.696128065 Simplifying x = -7.696128065Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.796128065, -7.696128065}
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