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Simplifying 0 = x2 + 12x + 0.0000018 Reorder the terms: 0 = 0.0000018 + 12x + x2 Solving 0 = 0.0000018 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + -0.0000018 = -0.0000018 -0.0000018 + -12x + -1x2 = 0.0000018 + 12x + x2 + -0.0000018 + -12x + -1x2 Reorder the terms: -0.0000018 + -12x + -1x2 = 0.0000018 + -0.0000018 + 12x + -12x + x2 + -1x2 Combine like terms: 0.0000018 + -0.0000018 = 0.0000000 -0.0000018 + -12x + -1x2 = 0.0000000 + 12x + -12x + x2 + -1x2 -0.0000018 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -0.0000018 + -12x + -1x2 = 0 + x2 + -1x2 -0.0000018 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -0.0000018 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.0000018 + 12x + x2 = 0 Move the constant term to the right: Add '-0.0000018' to each side of the equation. 0.0000018 + 12x + -0.0000018 + x2 = 0 + -0.0000018 Reorder the terms: 0.0000018 + -0.0000018 + 12x + x2 = 0 + -0.0000018 Combine like terms: 0.0000018 + -0.0000018 = 0.0000000 0.0000000 + 12x + x2 = 0 + -0.0000018 12x + x2 = 0 + -0.0000018 Combine like terms: 0 + -0.0000018 = -0.0000018 12x + x2 = -0.0000018 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -0.0000018 + 36 Reorder the terms: 36 + 12x + x2 = -0.0000018 + 36 Combine like terms: -0.0000018 + 36 = 35.9999982 36 + 12x + x2 = 35.9999982 Factor a perfect square on the left side: (x + 6)(x + 6) = 35.9999982 Calculate the square root of the right side: 5.99999985 Break this problem into two subproblems by setting (x + 6) equal to 5.99999985 and -5.99999985.Subproblem 1
x + 6 = 5.99999985 Simplifying x + 6 = 5.99999985 Reorder the terms: 6 + x = 5.99999985 Solving 6 + x = 5.99999985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.99999985 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.99999985 + -6 x = 5.99999985 + -6 Combine like terms: 5.99999985 + -6 = -0.00000015 x = -0.00000015 Simplifying x = -0.00000015Subproblem 2
x + 6 = -5.99999985 Simplifying x + 6 = -5.99999985 Reorder the terms: 6 + x = -5.99999985 Solving 6 + x = -5.99999985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.99999985 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.99999985 + -6 x = -5.99999985 + -6 Combine like terms: -5.99999985 + -6 = -11.99999985 x = -11.99999985 Simplifying x = -11.99999985Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.00000015, -11.99999985}
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