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Simplifying (x + -0.5)(x + -1.25) = 0 Reorder the terms: (-0.5 + x)(x + -1.25) = 0 Reorder the terms: (-0.5 + x)(-1.25 + x) = 0 Multiply (-0.5 + x) * (-1.25 + x) (-0.5(-1.25 + x) + x(-1.25 + x)) = 0 ((-1.25 * -0.5 + x * -0.5) + x(-1.25 + x)) = 0 ((0.625 + -0.5x) + x(-1.25 + x)) = 0 (0.625 + -0.5x + (-1.25 * x + x * x)) = 0 (0.625 + -0.5x + (-1.25x + x2)) = 0 Combine like terms: -0.5x + -1.25x = -1.75x (0.625 + -1.75x + x2) = 0 Solving 0.625 + -1.75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -1.75x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -1.75x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -1.75x + x2 = 0 + -0.625 -1.75x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -1.75x + x2 = -0.625 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = -0.625 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = -0.625 + 0.765625 Combine like terms: -0.625 + 0.765625 = 0.140625 0.765625 + -1.75x + x2 = 0.140625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 0.140625 Calculate the square root of the right side: 0.375 Break this problem into two subproblems by setting (x + -0.875) equal to 0.375 and -0.375.Subproblem 1
x + -0.875 = 0.375 Simplifying x + -0.875 = 0.375 Reorder the terms: -0.875 + x = 0.375 Solving -0.875 + x = 0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 0.375 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 0.375 + 0.875 x = 0.375 + 0.875 Combine like terms: 0.375 + 0.875 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + -0.875 = -0.375 Simplifying x + -0.875 = -0.375 Reorder the terms: -0.875 + x = -0.375 Solving -0.875 + x = -0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -0.375 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -0.375 + 0.875 x = -0.375 + 0.875 Combine like terms: -0.375 + 0.875 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, 0.5}
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