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Simplifying (-1x2) + (0.000000000112) + -1(0.00000000056x) = 0 (-1x2) + 0.000000000112 + -1(0.00000000056x) = 0 Remove parenthesis around (0.00000000056x) (-1x2) + 0.000000000112 + -1 * 0.00000000056x = 0 Multiply -1 * 0.00000000056 (-1x2) + 0.000000000112 + -0.00000000056x = 0 Reorder the terms: 0.000000000112 + -0.00000000056x + (-1x2) = 0 Solving 0.000000000112 + -0.00000000056x + (-1x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.000000000112 + 0.00000000056x + x2 = 0 Move the constant term to the right: Add '0.000000000112' to each side of the equation. -0.000000000112 + 0.00000000056x + 0.000000000112 + x2 = 0 + 0.000000000112 Reorder the terms: -0.000000000112 + 0.000000000112 + 0.00000000056x + x2 = 0 + 0.000000000112 Combine like terms: -0.000000000112 + 0.000000000112 = 0.000000000000 0.000000000000 + 0.00000000056x + x2 = 0 + 0.000000000112 0.00000000056x + x2 = 0 + 0.000000000112 Combine like terms: 0 + 0.000000000112 = 0.000000000112 0.00000000056x + x2 = 0.000000000112 The x term is 0.00000000056x. Take half its coefficient (0.00000000028). Square it (0.0000000000000000000784) and add it to both sides. Add '0.0000000000000000000784' to each side of the equation. 0.00000000056x + 0.0000000000000000000784 + x2 = 0.000000000112 + 0.0000000000000000000784 Reorder the terms: 0.0000000000000000000784 + 0.00000000056x + x2 = 0.000000000112 + 0.0000000000000000000784 Combine like terms: 0.000000000112 + 0.0000000000000000000784 = 0.0000000001120000000784 0.0000000000000000000784 + 0.00000000056x + x2 = 0.0000000001120000000784 Factor a perfect square on the left side: ((x) + 0.00000000028)((x) + 0.00000000028) = 0.0000000001120000000784 Calculate the square root of the right side: 0.000010583 Break this problem into two subproblems by setting ((x) + 0.00000000028) equal to 0.000010583 and -0.000010583.Subproblem 1
(x) + 0.00000000028 = 0.000010583 Simplifying (x) + 0.00000000028 = 0.000010583 x + 0.00000000028 = 0.000010583 Reorder the terms: 0.00000000028 + x = 0.000010583 Solving 0.00000000028 + x = 0.000010583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000000028' to each side of the equation. 0.00000000028 + -0.00000000028 + x = 0.000010583 + -0.00000000028 Combine like terms: 0.00000000028 + -0.00000000028 = 0.00000000000 0.00000000000 + x = 0.000010583 + -0.00000000028 x = 0.000010583 + -0.00000000028 Combine like terms: 0.000010583 + -0.00000000028 = 0.00001058272 x = 0.00001058272 Simplifying x = 0.00001058272Subproblem 2
(x) + 0.00000000028 = -0.000010583 Simplifying (x) + 0.00000000028 = -0.000010583 x + 0.00000000028 = -0.000010583 Reorder the terms: 0.00000000028 + x = -0.000010583 Solving 0.00000000028 + x = -0.000010583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000000028' to each side of the equation. 0.00000000028 + -0.00000000028 + x = -0.000010583 + -0.00000000028 Combine like terms: 0.00000000028 + -0.00000000028 = 0.00000000000 0.00000000000 + x = -0.000010583 + -0.00000000028 x = -0.000010583 + -0.00000000028 Combine like terms: -0.000010583 + -0.00000000028 = -0.00001058328 x = -0.00001058328 Simplifying x = -0.00001058328Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00001058272, -0.00001058328}
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