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Simplifying (25x2) + -1(112.5x) + 125 = x2 Remove parenthesis around (112.5x) (25x2) + -1 * 112.5x + 125 = x2 Multiply -1 * 112.5 (25x2) + -112.5x + 125 = x2 Reorder the terms: 125 + -112.5x + (25x2) = x2 Solving 125 + -112.5x + (25x2) = x2 Solving for variable 'x'. Combine like terms: (25x2) + -1x2 = 24x2 125 + -112.5x + 24x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 125 + -112.5x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 5.208333333 + -4.6875x + x2 = 0 Move the constant term to the right: Add '-5.208333333' to each side of the equation. 5.208333333 + -4.6875x + -5.208333333 + x2 = 0 + -5.208333333 Reorder the terms: 5.208333333 + -5.208333333 + -4.6875x + x2 = 0 + -5.208333333 Combine like terms: 5.208333333 + -5.208333333 = 0.000000000 0.000000000 + -4.6875x + x2 = 0 + -5.208333333 -4.6875x + x2 = 0 + -5.208333333 Combine like terms: 0 + -5.208333333 = -5.208333333 -4.6875x + x2 = -5.208333333 The x term is -4.6875x. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875x + 5.493164063 + x2 = -5.208333333 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875x + x2 = -5.208333333 + 5.493164063 Combine like terms: -5.208333333 + 5.493164063 = 0.28483073 5.493164063 + -4.6875x + x2 = 0.28483073 Factor a perfect square on the left side: (x + -2.34375)(x + -2.34375) = 0.28483073 Calculate the square root of the right side: 0.533695353 Break this problem into two subproblems by setting (x + -2.34375) equal to 0.533695353 and -0.533695353.Subproblem 1
x + -2.34375 = 0.533695353 Simplifying x + -2.34375 = 0.533695353 Reorder the terms: -2.34375 + x = 0.533695353 Solving -2.34375 + x = 0.533695353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + x = 0.533695353 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = 0.533695353 + 2.34375 x = 0.533695353 + 2.34375 Combine like terms: 0.533695353 + 2.34375 = 2.877445353 x = 2.877445353 Simplifying x = 2.877445353Subproblem 2
x + -2.34375 = -0.533695353 Simplifying x + -2.34375 = -0.533695353 Reorder the terms: -2.34375 + x = -0.533695353 Solving -2.34375 + x = -0.533695353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + x = -0.533695353 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = -0.533695353 + 2.34375 x = -0.533695353 + 2.34375 Combine like terms: -0.533695353 + 2.34375 = 1.810054647 x = 1.810054647 Simplifying x = 1.810054647Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.877445353, 1.810054647}
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