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Simplifying x2 + -2.5x + 0.16 = 0 Reorder the terms: 0.16 + -2.5x + x2 = 0 Solving 0.16 + -2.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -2.5x + -0.16 + x2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -2.5x + x2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -2.5x + x2 = 0 + -0.16 -2.5x + x2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -2.5x + x2 = -0.16 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.16 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.16 + 1.5625 Combine like terms: -0.16 + 1.5625 = 1.4025 1.5625 + -2.5x + x2 = 1.4025 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.4025 Calculate the square root of the right side: 1.184271928 Break this problem into two subproblems by setting (x + -1.25) equal to 1.184271928 and -1.184271928.Subproblem 1
x + -1.25 = 1.184271928 Simplifying x + -1.25 = 1.184271928 Reorder the terms: -1.25 + x = 1.184271928 Solving -1.25 + x = 1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.184271928 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.184271928 + 1.25 x = 1.184271928 + 1.25 Combine like terms: 1.184271928 + 1.25 = 2.434271928 x = 2.434271928 Simplifying x = 2.434271928Subproblem 2
x + -1.25 = -1.184271928 Simplifying x + -1.25 = -1.184271928 Reorder the terms: -1.25 + x = -1.184271928 Solving -1.25 + x = -1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.184271928 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.184271928 + 1.25 x = -1.184271928 + 1.25 Combine like terms: -1.184271928 + 1.25 = 0.065728072 x = 0.065728072 Simplifying x = 0.065728072Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.434271928, 0.065728072}
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