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Simplifying 0.018x2 + 1.656x + 4.4 = 0 Reorder the terms: 4.4 + 1.656x + 0.018x2 = 0 Solving 4.4 + 1.656x + 0.018x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.018 the coefficient of the squared term: Divide each side by '0.018'. 244.4444444 + 92x + x2 = 0 Move the constant term to the right: Add '-244.4444444' to each side of the equation. 244.4444444 + 92x + -244.4444444 + x2 = 0 + -244.4444444 Reorder the terms: 244.4444444 + -244.4444444 + 92x + x2 = 0 + -244.4444444 Combine like terms: 244.4444444 + -244.4444444 = 0.0000000 0.0000000 + 92x + x2 = 0 + -244.4444444 92x + x2 = 0 + -244.4444444 Combine like terms: 0 + -244.4444444 = -244.4444444 92x + x2 = -244.4444444 The x term is 92x. Take half its coefficient (46). Square it (2116) and add it to both sides. Add '2116' to each side of the equation. 92x + 2116 + x2 = -244.4444444 + 2116 Reorder the terms: 2116 + 92x + x2 = -244.4444444 + 2116 Combine like terms: -244.4444444 + 2116 = 1871.5555556 2116 + 92x + x2 = 1871.5555556 Factor a perfect square on the left side: (x + 46)(x + 46) = 1871.5555556 Calculate the square root of the right side: 43.261478888 Break this problem into two subproblems by setting (x + 46) equal to 43.261478888 and -43.261478888.Subproblem 1
x + 46 = 43.261478888 Simplifying x + 46 = 43.261478888 Reorder the terms: 46 + x = 43.261478888 Solving 46 + x = 43.261478888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = 43.261478888 + -46 Combine like terms: 46 + -46 = 0 0 + x = 43.261478888 + -46 x = 43.261478888 + -46 Combine like terms: 43.261478888 + -46 = -2.738521112 x = -2.738521112 Simplifying x = -2.738521112Subproblem 2
x + 46 = -43.261478888 Simplifying x + 46 = -43.261478888 Reorder the terms: 46 + x = -43.261478888 Solving 46 + x = -43.261478888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = -43.261478888 + -46 Combine like terms: 46 + -46 = 0 0 + x = -43.261478888 + -46 x = -43.261478888 + -46 Combine like terms: -43.261478888 + -46 = -89.261478888 x = -89.261478888 Simplifying x = -89.261478888Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.738521112, -89.261478888}
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