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Simplifying x2 + -2.0125x + 1.01 = 0 Reorder the terms: 1.01 + -2.0125x + x2 = 0 Solving 1.01 + -2.0125x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.01' to each side of the equation. 1.01 + -2.0125x + -1.01 + x2 = 0 + -1.01 Reorder the terms: 1.01 + -1.01 + -2.0125x + x2 = 0 + -1.01 Combine like terms: 1.01 + -1.01 = 0.00 0.00 + -2.0125x + x2 = 0 + -1.01 -2.0125x + x2 = 0 + -1.01 Combine like terms: 0 + -1.01 = -1.01 -2.0125x + x2 = -1.01 The x term is -2.0125x. Take half its coefficient (-1.00625). Square it (1.012539063) and add it to both sides. Add '1.012539063' to each side of the equation. -2.0125x + 1.012539063 + x2 = -1.01 + 1.012539063 Reorder the terms: 1.012539063 + -2.0125x + x2 = -1.01 + 1.012539063 Combine like terms: -1.01 + 1.012539063 = 0.002539063 1.012539063 + -2.0125x + x2 = 0.002539063 Factor a perfect square on the left side: (x + -1.00625)(x + -1.00625) = 0.002539063 Calculate the square root of the right side: 0.050389116 Break this problem into two subproblems by setting (x + -1.00625) equal to 0.050389116 and -0.050389116.Subproblem 1
x + -1.00625 = 0.050389116 Simplifying x + -1.00625 = 0.050389116 Reorder the terms: -1.00625 + x = 0.050389116 Solving -1.00625 + x = 0.050389116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.00625' to each side of the equation. -1.00625 + 1.00625 + x = 0.050389116 + 1.00625 Combine like terms: -1.00625 + 1.00625 = 0.00000 0.00000 + x = 0.050389116 + 1.00625 x = 0.050389116 + 1.00625 Combine like terms: 0.050389116 + 1.00625 = 1.056639116 x = 1.056639116 Simplifying x = 1.056639116Subproblem 2
x + -1.00625 = -0.050389116 Simplifying x + -1.00625 = -0.050389116 Reorder the terms: -1.00625 + x = -0.050389116 Solving -1.00625 + x = -0.050389116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.00625' to each side of the equation. -1.00625 + 1.00625 + x = -0.050389116 + 1.00625 Combine like terms: -1.00625 + 1.00625 = 0.00000 0.00000 + x = -0.050389116 + 1.00625 x = -0.050389116 + 1.00625 Combine like terms: -0.050389116 + 1.00625 = 0.955860884 x = 0.955860884 Simplifying x = 0.955860884Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.056639116, 0.955860884}
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