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Simplifying (10000000)(x2) + 13x + -1.3 = 0 Reorder the terms: -1.3 + 13x + 10000000x2 = 0 Solving -1.3 + 13x + 10000000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10000000 the coefficient of the squared term: Divide each side by '10000000'. -0.00000013 + 0.0000013x + x2 = 0 Move the constant term to the right: Add '0.00000013' to each side of the equation. -0.00000013 + 0.0000013x + 0.00000013 + x2 = 0 + 0.00000013 Reorder the terms: -0.00000013 + 0.00000013 + 0.0000013x + x2 = 0 + 0.00000013 Combine like terms: -0.00000013 + 0.00000013 = 0.00000000 0.00000000 + 0.0000013x + x2 = 0 + 0.00000013 0.0000013x + x2 = 0 + 0.00000013 Combine like terms: 0 + 0.00000013 = 0.00000013 0.0000013x + x2 = 0.00000013 The x term is 0.0000013x. Take half its coefficient (0.00000065). Square it (0.0000000000004225) and add it to both sides. Add '0.0000000000004225' to each side of the equation. 0.0000013x + 0.0000000000004225 + x2 = 0.00000013 + 0.0000000000004225 Reorder the terms: 0.0000000000004225 + 0.0000013x + x2 = 0.00000013 + 0.0000000000004225 Combine like terms: 0.00000013 + 0.0000000000004225 = 0.0000001300004225 0.0000000000004225 + 0.0000013x + x2 = 0.0000001300004225 Factor a perfect square on the left side: (x + 0.00000065)(x + 0.00000065) = 0.0000001300004225 Calculate the square root of the right side: 0.000360556 Break this problem into two subproblems by setting (x + 0.00000065) equal to 0.000360556 and -0.000360556.Subproblem 1
x + 0.00000065 = 0.000360556 Simplifying x + 0.00000065 = 0.000360556 Reorder the terms: 0.00000065 + x = 0.000360556 Solving 0.00000065 + x = 0.000360556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000065' to each side of the equation. 0.00000065 + -0.00000065 + x = 0.000360556 + -0.00000065 Combine like terms: 0.00000065 + -0.00000065 = 0.00000000 0.00000000 + x = 0.000360556 + -0.00000065 x = 0.000360556 + -0.00000065 Combine like terms: 0.000360556 + -0.00000065 = 0.000359906 x = 0.000359906 Simplifying x = 0.000359906Subproblem 2
x + 0.00000065 = -0.000360556 Simplifying x + 0.00000065 = -0.000360556 Reorder the terms: 0.00000065 + x = -0.000360556 Solving 0.00000065 + x = -0.000360556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000065' to each side of the equation. 0.00000065 + -0.00000065 + x = -0.000360556 + -0.00000065 Combine like terms: 0.00000065 + -0.00000065 = 0.00000000 0.00000000 + x = -0.000360556 + -0.00000065 x = -0.000360556 + -0.00000065 Combine like terms: -0.000360556 + -0.00000065 = -0.000361206 x = -0.000361206 Simplifying x = -0.000361206Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000359906, -0.000361206}
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