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Simplifying 10000000000x2 + 5.6x + -1.12 = 0 Reorder the terms: -1.12 + 5.6x + 10000000000x2 = 0 Solving -1.12 + 5.6x + 10000000000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10000000000 the coefficient of the squared term: Divide each side by '10000000000'. -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 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 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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