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Simplifying x2 + -2.5x + 1.56 = 0 Reorder the terms: 1.56 + -2.5x + x2 = 0 Solving 1.56 + -2.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.56' to each side of the equation. 1.56 + -2.5x + -1.56 + x2 = 0 + -1.56 Reorder the terms: 1.56 + -1.56 + -2.5x + x2 = 0 + -1.56 Combine like terms: 1.56 + -1.56 = 0.00 0.00 + -2.5x + x2 = 0 + -1.56 -2.5x + x2 = 0 + -1.56 Combine like terms: 0 + -1.56 = -1.56 -2.5x + x2 = -1.56 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 = -1.56 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.56 + 1.5625 Combine like terms: -1.56 + 1.5625 = 0.0025 1.5625 + -2.5x + x2 = 0.0025 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + -1.25) equal to 0.05 and -0.05.Subproblem 1
x + -1.25 = 0.05 Simplifying x + -1.25 = 0.05 Reorder the terms: -1.25 + x = 0.05 Solving -1.25 + x = 0.05 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 = 0.05 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.05 + 1.25 x = 0.05 + 1.25 Combine like terms: 0.05 + 1.25 = 1.3 x = 1.3 Simplifying x = 1.3Subproblem 2
x + -1.25 = -0.05 Simplifying x + -1.25 = -0.05 Reorder the terms: -1.25 + x = -0.05 Solving -1.25 + x = -0.05 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 = -0.05 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.05 + 1.25 x = -0.05 + 1.25 Combine like terms: -0.05 + 1.25 = 1.2 x = 1.2 Simplifying x = 1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3, 1.2}
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