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Simplifying x2 + 0.75x + 0.06 = 0 Reorder the terms: 0.06 + 0.75x + x2 = 0 Solving 0.06 + 0.75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.06' to each side of the equation. 0.06 + 0.75x + -0.06 + x2 = 0 + -0.06 Reorder the terms: 0.06 + -0.06 + 0.75x + x2 = 0 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + 0.75x + x2 = 0 + -0.06 0.75x + x2 = 0 + -0.06 Combine like terms: 0 + -0.06 = -0.06 0.75x + x2 = -0.06 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 = -0.06 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -0.06 + 0.140625 Combine like terms: -0.06 + 0.140625 = 0.080625 0.140625 + 0.75x + x2 = 0.080625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.080625 Calculate the square root of the right side: 0.283945417 Break this problem into two subproblems by setting (x + 0.375) equal to 0.283945417 and -0.283945417.Subproblem 1
x + 0.375 = 0.283945417 Simplifying x + 0.375 = 0.283945417 Reorder the terms: 0.375 + x = 0.283945417 Solving 0.375 + x = 0.283945417 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 = 0.283945417 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.283945417 + -0.375 x = 0.283945417 + -0.375 Combine like terms: 0.283945417 + -0.375 = -0.091054583 x = -0.091054583 Simplifying x = -0.091054583Subproblem 2
x + 0.375 = -0.283945417 Simplifying x + 0.375 = -0.283945417 Reorder the terms: 0.375 + x = -0.283945417 Solving 0.375 + x = -0.283945417 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 = -0.283945417 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.283945417 + -0.375 x = -0.283945417 + -0.375 Combine like terms: -0.283945417 + -0.375 = -0.658945417 x = -0.658945417 Simplifying x = -0.658945417Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.091054583, -0.658945417}
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