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Simplifying x2 + 0.1x + -0.0625 = 0 Reorder the terms: -0.0625 + 0.1x + x2 = 0 Solving -0.0625 + 0.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.1x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.1x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.1x + x2 = 0 + 0.0625 0.1x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.1x + x2 = 0.0625 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.0625 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.0625 + 0.0025 Combine like terms: 0.0625 + 0.0025 = 0.065 0.0025 + 0.1x + x2 = 0.065 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.065 Calculate the square root of the right side: 0.254950976 Break this problem into two subproblems by setting (x + 0.05) equal to 0.254950976 and -0.254950976.Subproblem 1
x + 0.05 = 0.254950976 Simplifying x + 0.05 = 0.254950976 Reorder the terms: 0.05 + x = 0.254950976 Solving 0.05 + x = 0.254950976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.254950976 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.254950976 + -0.05 x = 0.254950976 + -0.05 Combine like terms: 0.254950976 + -0.05 = 0.204950976 x = 0.204950976 Simplifying x = 0.204950976Subproblem 2
x + 0.05 = -0.254950976 Simplifying x + 0.05 = -0.254950976 Reorder the terms: 0.05 + x = -0.254950976 Solving 0.05 + x = -0.254950976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.254950976 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.254950976 + -0.05 x = -0.254950976 + -0.05 Combine like terms: -0.254950976 + -0.05 = -0.304950976 x = -0.304950976 Simplifying x = -0.304950976Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.204950976, -0.304950976}
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