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Simplifying (0.00001105) + -1(0.00001105x) + -4x2 = 0 0.00001105 + -1(0.00001105x) + -4x2 = 0 Remove parenthesis around (0.00001105x) 0.00001105 + -1 * 0.00001105x + -4x2 = 0 Multiply -1 * 0.00001105 0.00001105 + -0.00001105x + -4x2 = 0 Solving 0.00001105 + -0.00001105x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.0000027625 + 0.0000027625x + x2 = 0 Move the constant term to the right: Add '0.0000027625' to each side of the equation. -0.0000027625 + 0.0000027625x + 0.0000027625 + x2 = 0 + 0.0000027625 Reorder the terms: -0.0000027625 + 0.0000027625 + 0.0000027625x + x2 = 0 + 0.0000027625 Combine like terms: -0.0000027625 + 0.0000027625 = 0.0000000000 0.0000000000 + 0.0000027625x + x2 = 0 + 0.0000027625 0.0000027625x + x2 = 0 + 0.0000027625 Combine like terms: 0 + 0.0000027625 = 0.0000027625 0.0000027625x + x2 = 0.0000027625 The x term is 0.0000027625x. Take half its coefficient (0.00000138125). Square it (0.000000000001907851563) and add it to both sides. Add '0.000000000001907851563' to each side of the equation. 0.0000027625x + 0.000000000001907851563 + x2 = 0.0000027625 + 0.000000000001907851563 Reorder the terms: 0.000000000001907851563 + 0.0000027625x + x2 = 0.0000027625 + 0.000000000001907851563 Combine like terms: 0.0000027625 + 0.000000000001907851563 = 0.000002762501907851563 0.000000000001907851563 + 0.0000027625x + x2 = 0.000002762501907851563 Factor a perfect square on the left side: (x + 0.00000138125)(x + 0.00000138125) = 0.000002762501907851563 Calculate the square root of the right side: 0.001662078 Break this problem into two subproblems by setting (x + 0.00000138125) equal to 0.001662078 and -0.001662078.Subproblem 1
x + 0.00000138125 = 0.001662078 Simplifying x + 0.00000138125 = 0.001662078 Reorder the terms: 0.00000138125 + x = 0.001662078 Solving 0.00000138125 + x = 0.001662078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000138125' to each side of the equation. 0.00000138125 + -0.00000138125 + x = 0.001662078 + -0.00000138125 Combine like terms: 0.00000138125 + -0.00000138125 = 0.00000000000 0.00000000000 + x = 0.001662078 + -0.00000138125 x = 0.001662078 + -0.00000138125 Combine like terms: 0.001662078 + -0.00000138125 = 0.00166069675 x = 0.00166069675 Simplifying x = 0.00166069675Subproblem 2
x + 0.00000138125 = -0.001662078 Simplifying x + 0.00000138125 = -0.001662078 Reorder the terms: 0.00000138125 + x = -0.001662078 Solving 0.00000138125 + x = -0.001662078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000138125' to each side of the equation. 0.00000138125 + -0.00000138125 + x = -0.001662078 + -0.00000138125 Combine like terms: 0.00000138125 + -0.00000138125 = 0.00000000000 0.00000000000 + x = -0.001662078 + -0.00000138125 x = -0.001662078 + -0.00000138125 Combine like terms: -0.001662078 + -0.00000138125 = -0.00166345925 x = -0.00166345925 Simplifying x = -0.00166345925Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00166069675, -0.00166345925}
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