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Simplifying 2x2 + -1.5x + -0.5 = 0 Reorder the terms: -0.5 + -1.5x + 2x2 = 0 Solving -0.5 + -1.5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.75x + x2 = 0 + 0.25 -0.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.75x + x2 = 0.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.25 + 0.140625 Combine like terms: 0.25 + 0.140625 = 0.390625 0.140625 + -0.75x + x2 = 0.390625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.390625 Calculate the square root of the right side: 0.625 Break this problem into two subproblems by setting (x + -0.375) equal to 0.625 and -0.625.Subproblem 1
x + -0.375 = 0.625 Simplifying x + -0.375 = 0.625 Reorder the terms: -0.375 + x = 0.625 Solving -0.375 + x = 0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.625 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.625 + 0.375 x = 0.625 + 0.375 Combine like terms: 0.625 + 0.375 = 1 x = 1 Simplifying x = 1Subproblem 2
x + -0.375 = -0.625 Simplifying x + -0.375 = -0.625 Reorder the terms: -0.375 + x = -0.625 Solving -0.375 + x = -0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.625 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.625 + 0.375 x = -0.625 + 0.375 Combine like terms: -0.625 + 0.375 = -0.25 x = -0.25 Simplifying x = -0.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -0.25}
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