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Simplifying 0 = x2 + 0.250x + -0.125 Reorder the terms: 0 = -0.125 + 0.250x + x2 Solving 0 = -0.125 + 0.250x + x2 Solving for variable 'x'. Combine like terms: 0 + 0.125 = 0.125 0.125 + -0.250x + -1x2 = -0.125 + 0.250x + x2 + 0.125 + -0.250x + -1x2 Reorder the terms: 0.125 + -0.250x + -1x2 = -0.125 + 0.125 + 0.250x + -0.250x + x2 + -1x2 Combine like terms: -0.125 + 0.125 = 0.000 0.125 + -0.250x + -1x2 = 0.000 + 0.250x + -0.250x + x2 + -1x2 0.125 + -0.250x + -1x2 = 0.250x + -0.250x + x2 + -1x2 Combine like terms: 0.250x + -0.250x = 0.000 0.125 + -0.250x + -1x2 = 0.000 + x2 + -1x2 0.125 + -0.250x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.125 + -0.250x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.125 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.25x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.25x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.25x + x2 = 0 + 0.125 0.25x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.25x + x2 = 0.125 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.125 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.125 + 0.015625 Combine like terms: 0.125 + 0.015625 = 0.140625 0.015625 + 0.25x + x2 = 0.140625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.140625 Calculate the square root of the right side: 0.375 Break this problem into two subproblems by setting (x + 0.125) equal to 0.375 and -0.375.Subproblem 1
x + 0.125 = 0.375 Simplifying x + 0.125 = 0.375 Reorder the terms: 0.125 + x = 0.375 Solving 0.125 + x = 0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.375 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.375 + -0.125 x = 0.375 + -0.125 Combine like terms: 0.375 + -0.125 = 0.25 x = 0.25 Simplifying x = 0.25Subproblem 2
x + 0.125 = -0.375 Simplifying x + 0.125 = -0.375 Reorder the terms: 0.125 + x = -0.375 Solving 0.125 + x = -0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.375 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.375 + -0.125 x = -0.375 + -0.125 Combine like terms: -0.375 + -0.125 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25, -0.5}
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