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Simplifying 0.012x2 + 0.1x + 0.18 = 0 Reorder the terms: 0.18 + 0.1x + 0.012x2 = 0 Solving 0.18 + 0.1x + 0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. 15 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 8.333333333x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 8.333333333x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 8.333333333x + x2 = 0 + -15 8.333333333x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 8.333333333x + x2 = -15 The x term is 8.333333333x. Take half its coefficient (4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. 8.333333333x + 17.36111111 + x2 = -15 + 17.36111111 Reorder the terms: 17.36111111 + 8.333333333x + x2 = -15 + 17.36111111 Combine like terms: -15 + 17.36111111 = 2.36111111 17.36111111 + 8.333333333x + x2 = 2.36111111 Factor a perfect square on the left side: (x + 4.166666667)(x + 4.166666667) = 2.36111111 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x + 4.166666667) equal to 1.536590743 and -1.536590743.Subproblem 1
x + 4.166666667 = 1.536590743 Simplifying x + 4.166666667 = 1.536590743 Reorder the terms: 4.166666667 + x = 1.536590743 Solving 4.166666667 + x = 1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 1.536590743 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 1.536590743 + -4.166666667 x = 1.536590743 + -4.166666667 Combine like terms: 1.536590743 + -4.166666667 = -2.630075924 x = -2.630075924 Simplifying x = -2.630075924Subproblem 2
x + 4.166666667 = -1.536590743 Simplifying x + 4.166666667 = -1.536590743 Reorder the terms: 4.166666667 + x = -1.536590743 Solving 4.166666667 + x = -1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -1.536590743 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -1.536590743 + -4.166666667 x = -1.536590743 + -4.166666667 Combine like terms: -1.536590743 + -4.166666667 = -5.70325741 x = -5.70325741 Simplifying x = -5.70325741Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.630075924, -5.70325741}
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