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Simplifying (0.00001105) + -1(0.00001105x) + -2x2 = 0 0.00001105 + -1(0.00001105x) + -2x2 = 0 Remove parenthesis around (0.00001105x) 0.00001105 + -1 * 0.00001105x + -2x2 = 0 Multiply -1 * 0.00001105 0.00001105 + -0.00001105x + -2x2 = 0 Solving 0.00001105 + -0.00001105x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.000005525 + 0.000005525x + x2 = 0 Move the constant term to the right: Add '0.000005525' to each side of the equation. -0.000005525 + 0.000005525x + 0.000005525 + x2 = 0 + 0.000005525 Reorder the terms: -0.000005525 + 0.000005525 + 0.000005525x + x2 = 0 + 0.000005525 Combine like terms: -0.000005525 + 0.000005525 = 0.000000000 0.000000000 + 0.000005525x + x2 = 0 + 0.000005525 0.000005525x + x2 = 0 + 0.000005525 Combine like terms: 0 + 0.000005525 = 0.000005525 0.000005525x + x2 = 0.000005525 The x term is 0.000005525x. Take half its coefficient (0.0000027625). Square it (0.00000000000763140625) and add it to both sides. Add '0.00000000000763140625' to each side of the equation. 0.000005525x + 0.00000000000763140625 + x2 = 0.000005525 + 0.00000000000763140625 Reorder the terms: 0.00000000000763140625 + 0.000005525x + x2 = 0.000005525 + 0.00000000000763140625 Combine like terms: 0.000005525 + 0.00000000000763140625 = 0.00000552500763140625 0.00000000000763140625 + 0.000005525x + x2 = 0.00000552500763140625 Factor a perfect square on the left side: (x + 0.0000027625)(x + 0.0000027625) = 0.00000552500763140625 Calculate the square root of the right side: 0.002350533 Break this problem into two subproblems by setting (x + 0.0000027625) equal to 0.002350533 and -0.002350533.Subproblem 1
x + 0.0000027625 = 0.002350533 Simplifying x + 0.0000027625 = 0.002350533 Reorder the terms: 0.0000027625 + x = 0.002350533 Solving 0.0000027625 + x = 0.002350533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000027625' to each side of the equation. 0.0000027625 + -0.0000027625 + x = 0.002350533 + -0.0000027625 Combine like terms: 0.0000027625 + -0.0000027625 = 0.0000000000 0.0000000000 + x = 0.002350533 + -0.0000027625 x = 0.002350533 + -0.0000027625 Combine like terms: 0.002350533 + -0.0000027625 = 0.0023477705 x = 0.0023477705 Simplifying x = 0.0023477705Subproblem 2
x + 0.0000027625 = -0.002350533 Simplifying x + 0.0000027625 = -0.002350533 Reorder the terms: 0.0000027625 + x = -0.002350533 Solving 0.0000027625 + x = -0.002350533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000027625' to each side of the equation. 0.0000027625 + -0.0000027625 + x = -0.002350533 + -0.0000027625 Combine like terms: 0.0000027625 + -0.0000027625 = 0.0000000000 0.0000000000 + x = -0.002350533 + -0.0000027625 x = -0.002350533 + -0.0000027625 Combine like terms: -0.002350533 + -0.0000027625 = -0.0023532955 x = -0.0023532955 Simplifying x = -0.0023532955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0023477705, -0.0023532955}
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