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Simplifying x2 + 0.250018x + -0.0000027 = 0 Reorder the terms: -0.0000027 + 0.250018x + x2 = 0 Solving -0.0000027 + 0.250018x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0000027' to each side of the equation. -0.0000027 + 0.250018x + 0.0000027 + x2 = 0 + 0.0000027 Reorder the terms: -0.0000027 + 0.0000027 + 0.250018x + x2 = 0 + 0.0000027 Combine like terms: -0.0000027 + 0.0000027 = 0.0000000 0.0000000 + 0.250018x + x2 = 0 + 0.0000027 0.250018x + x2 = 0 + 0.0000027 Combine like terms: 0 + 0.0000027 = 0.0000027 0.250018x + x2 = 0.0000027 The x term is 0.250018x. Take half its coefficient (0.125009). Square it (0.01562725008) and add it to both sides. Add '0.01562725008' to each side of the equation. 0.250018x + 0.01562725008 + x2 = 0.0000027 + 0.01562725008 Reorder the terms: 0.01562725008 + 0.250018x + x2 = 0.0000027 + 0.01562725008 Combine like terms: 0.0000027 + 0.01562725008 = 0.01562995008 0.01562725008 + 0.250018x + x2 = 0.01562995008 Factor a perfect square on the left side: (x + 0.125009)(x + 0.125009) = 0.01562995008 Calculate the square root of the right side: 0.125019799 Break this problem into two subproblems by setting (x + 0.125009) equal to 0.125019799 and -0.125019799.Subproblem 1
x + 0.125009 = 0.125019799 Simplifying x + 0.125009 = 0.125019799 Reorder the terms: 0.125009 + x = 0.125019799 Solving 0.125009 + x = 0.125019799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125009' to each side of the equation. 0.125009 + -0.125009 + x = 0.125019799 + -0.125009 Combine like terms: 0.125009 + -0.125009 = 0.000000 0.000000 + x = 0.125019799 + -0.125009 x = 0.125019799 + -0.125009 Combine like terms: 0.125019799 + -0.125009 = 0.000010799 x = 0.000010799 Simplifying x = 0.000010799Subproblem 2
x + 0.125009 = -0.125019799 Simplifying x + 0.125009 = -0.125019799 Reorder the terms: 0.125009 + x = -0.125019799 Solving 0.125009 + x = -0.125019799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125009' to each side of the equation. 0.125009 + -0.125009 + x = -0.125019799 + -0.125009 Combine like terms: 0.125009 + -0.125009 = 0.000000 0.000000 + x = -0.125019799 + -0.125009 x = -0.125019799 + -0.125009 Combine like terms: -0.125019799 + -0.125009 = -0.250028799 x = -0.250028799 Simplifying x = -0.250028799Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000010799, -0.250028799}
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