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Simplifying 2x2 + -0.5x = 0.125 Reorder the terms: -0.5x + 2x2 = 0.125 Solving -0.5x + 2x2 = 0.125 Solving for variable 'x'. Reorder the terms: -0.125 + -0.5x + 2x2 = 0.125 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 -0.125 + -0.5x + 2x2 = 0.000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.0625 + -0.25x + x2 = 0.000 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.25x + 0.0625 + x2 = 0.000 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.25x + x2 = 0.000 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.25x + x2 = 0.000 + 0.0625 -0.25x + x2 = 0.000 + 0.0625 Combine like terms: 0.000 + 0.0625 = 0.0625 -0.25x + x2 = 0.0625 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 = 0.0625 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.0625 + 0.015625 Combine like terms: 0.0625 + 0.015625 = 0.078125 0.015625 + -0.25x + x2 = 0.078125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.078125 Calculate the square root of the right side: 0.279508497 Break this problem into two subproblems by setting (x + -0.125) equal to 0.279508497 and -0.279508497.Subproblem 1
x + -0.125 = 0.279508497 Simplifying x + -0.125 = 0.279508497 Reorder the terms: -0.125 + x = 0.279508497 Solving -0.125 + x = 0.279508497 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 = 0.279508497 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.279508497 + 0.125 x = 0.279508497 + 0.125 Combine like terms: 0.279508497 + 0.125 = 0.404508497 x = 0.404508497 Simplifying x = 0.404508497Subproblem 2
x + -0.125 = -0.279508497 Simplifying x + -0.125 = -0.279508497 Reorder the terms: -0.125 + x = -0.279508497 Solving -0.125 + x = -0.279508497 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 = -0.279508497 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.279508497 + 0.125 x = -0.279508497 + 0.125 Combine like terms: -0.279508497 + 0.125 = -0.154508497 x = -0.154508497 Simplifying x = -0.154508497Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.404508497, -0.154508497}
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