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Simplifying (x2) + (0.000000000556) * x + -1(0.000000000556) = 0 x2 + (0.000000000556) * x + -1(0.000000000556) = 0 Multiply -1 * 0.000000000556 x2 + 0.000000000556x + -0.000000000556 = 0 Reorder the terms: -0.000000000556 + 0.000000000556x + x2 = 0 Solving -0.000000000556 + 0.000000000556x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.000000000556' to each side of the equation. -0.000000000556 + 0.000000000556x + 0.000000000556 + x2 = 0 + 0.000000000556 Reorder the terms: -0.000000000556 + 0.000000000556 + 0.000000000556x + x2 = 0 + 0.000000000556 Combine like terms: -0.000000000556 + 0.000000000556 = 0.000000000000 0.000000000000 + 0.000000000556x + x2 = 0 + 0.000000000556 0.000000000556x + x2 = 0 + 0.000000000556 Combine like terms: 0 + 0.000000000556 = 0.000000000556 0.000000000556x + x2 = 0.000000000556 The x term is 0.000000000556x. Take half its coefficient (0.000000000278). Square it (0.000000000000000000077284) and add it to both sides. Add '0.000000000000000000077284' to each side of the equation. 0.000000000556x + 0.000000000000000000077284 + x2 = 0.000000000556 + 0.000000000000000000077284 Reorder the terms: 0.000000000000000000077284 + 0.000000000556x + x2 = 0.000000000556 + 0.000000000000000000077284 Combine like terms: 0.000000000556 + 0.000000000000000000077284 = 0.000000000556000000077284 0.000000000000000000077284 + 0.000000000556x + x2 = 0.000000000556000000077284 Factor a perfect square on the left side: (x + 0.000000000278)(x + 0.000000000278) = 0.000000000556000000077284 Calculate the square root of the right side: 0.00002358 Break this problem into two subproblems by setting (x + 0.000000000278) equal to 0.00002358 and -0.00002358.Subproblem 1
x + 0.000000000278 = 0.00002358 Simplifying x + 0.000000000278 = 0.00002358 Reorder the terms: 0.000000000278 + x = 0.00002358 Solving 0.000000000278 + x = 0.00002358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000000000278' to each side of the equation. 0.000000000278 + -0.000000000278 + x = 0.00002358 + -0.000000000278 Combine like terms: 0.000000000278 + -0.000000000278 = 0.000000000000 0.000000000000 + x = 0.00002358 + -0.000000000278 x = 0.00002358 + -0.000000000278 Combine like terms: 0.00002358 + -0.000000000278 = 0.000023579722 x = 0.000023579722 Simplifying x = 0.000023579722Subproblem 2
x + 0.000000000278 = -0.00002358 Simplifying x + 0.000000000278 = -0.00002358 Reorder the terms: 0.000000000278 + x = -0.00002358 Solving 0.000000000278 + x = -0.00002358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000000000278' to each side of the equation. 0.000000000278 + -0.000000000278 + x = -0.00002358 + -0.000000000278 Combine like terms: 0.000000000278 + -0.000000000278 = 0.000000000000 0.000000000000 + x = -0.00002358 + -0.000000000278 x = -0.00002358 + -0.000000000278 Combine like terms: -0.00002358 + -0.000000000278 = -0.000023580278 x = -0.000023580278 Simplifying x = -0.000023580278Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000023579722, -0.000023580278}
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