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Simplifying 0.04x2 + -0.5x + 0.08 = 0 Reorder the terms: 0.08 + -0.5x + 0.04x2 = 0 Solving 0.08 + -0.5x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 2 + -12.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -12.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -12.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -12.5x + x2 = 0 + -2 -12.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -12.5x + x2 = -2 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -2 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -2 + 39.0625 Combine like terms: -2 + 39.0625 = 37.0625 39.0625 + -12.5x + x2 = 37.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 37.0625 Calculate the square root of the right side: 6.087897831 Break this problem into two subproblems by setting (x + -6.25) equal to 6.087897831 and -6.087897831.Subproblem 1
x + -6.25 = 6.087897831 Simplifying x + -6.25 = 6.087897831 Reorder the terms: -6.25 + x = 6.087897831 Solving -6.25 + x = 6.087897831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 6.087897831 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.087897831 + 6.25 x = 6.087897831 + 6.25 Combine like terms: 6.087897831 + 6.25 = 12.337897831 x = 12.337897831 Simplifying x = 12.337897831Subproblem 2
x + -6.25 = -6.087897831 Simplifying x + -6.25 = -6.087897831 Reorder the terms: -6.25 + x = -6.087897831 Solving -6.25 + x = -6.087897831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -6.087897831 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.087897831 + 6.25 x = -6.087897831 + 6.25 Combine like terms: -6.087897831 + 6.25 = 0.162102169 x = 0.162102169 Simplifying x = 0.162102169Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.337897831, 0.162102169}
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