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Simplifying 12 = 0.012x2 + 0.247x + 10.184 Reorder the terms: 12 = 10.184 + 0.247x + 0.012x2 Solving 12 = 10.184 + 0.247x + 0.012x2 Solving for variable 'x'. Combine like terms: 12 + -10.184 = 1.816 1.816 + -0.247x + -0.012x2 = 10.184 + 0.247x + 0.012x2 + -10.184 + -0.247x + -0.012x2 Reorder the terms: 1.816 + -0.247x + -0.012x2 = 10.184 + -10.184 + 0.247x + -0.247x + 0.012x2 + -0.012x2 Combine like terms: 10.184 + -10.184 = 0.000 1.816 + -0.247x + -0.012x2 = 0.000 + 0.247x + -0.247x + 0.012x2 + -0.012x2 1.816 + -0.247x + -0.012x2 = 0.247x + -0.247x + 0.012x2 + -0.012x2 Combine like terms: 0.247x + -0.247x = 0.000 1.816 + -0.247x + -0.012x2 = 0.000 + 0.012x2 + -0.012x2 1.816 + -0.247x + -0.012x2 = 0.012x2 + -0.012x2 Combine like terms: 0.012x2 + -0.012x2 = 0.000 1.816 + -0.247x + -0.012x2 = 0.000 Begin completing the square. Divide all terms by -0.012 the coefficient of the squared term: Divide each side by '-0.012'. -151.3333333 + 20.58333333x + x2 = 0 Move the constant term to the right: Add '151.3333333' to each side of the equation. -151.3333333 + 20.58333333x + 151.3333333 + x2 = 0 + 151.3333333 Reorder the terms: -151.3333333 + 151.3333333 + 20.58333333x + x2 = 0 + 151.3333333 Combine like terms: -151.3333333 + 151.3333333 = 0.0000000 0.0000000 + 20.58333333x + x2 = 0 + 151.3333333 20.58333333x + x2 = 0 + 151.3333333 Combine like terms: 0 + 151.3333333 = 151.3333333 20.58333333x + x2 = 151.3333333 The x term is 20.58333333x. Take half its coefficient (10.29166667). Square it (105.9184028) and add it to both sides. Add '105.9184028' to each side of the equation. 20.58333333x + 105.9184028 + x2 = 151.3333333 + 105.9184028 Reorder the terms: 105.9184028 + 20.58333333x + x2 = 151.3333333 + 105.9184028 Combine like terms: 151.3333333 + 105.9184028 = 257.2517361 105.9184028 + 20.58333333x + x2 = 257.2517361 Factor a perfect square on the left side: (x + 10.29166667)(x + 10.29166667) = 257.2517361 Calculate the square root of the right side: 16.039069053 Break this problem into two subproblems by setting (x + 10.29166667) equal to 16.039069053 and -16.039069053.Subproblem 1
x + 10.29166667 = 16.039069053 Simplifying x + 10.29166667 = 16.039069053 Reorder the terms: 10.29166667 + x = 16.039069053 Solving 10.29166667 + x = 16.039069053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.29166667' to each side of the equation. 10.29166667 + -10.29166667 + x = 16.039069053 + -10.29166667 Combine like terms: 10.29166667 + -10.29166667 = 0.00000000 0.00000000 + x = 16.039069053 + -10.29166667 x = 16.039069053 + -10.29166667 Combine like terms: 16.039069053 + -10.29166667 = 5.747402383 x = 5.747402383 Simplifying x = 5.747402383Subproblem 2
x + 10.29166667 = -16.039069053 Simplifying x + 10.29166667 = -16.039069053 Reorder the terms: 10.29166667 + x = -16.039069053 Solving 10.29166667 + x = -16.039069053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.29166667' to each side of the equation. 10.29166667 + -10.29166667 + x = -16.039069053 + -10.29166667 Combine like terms: 10.29166667 + -10.29166667 = 0.00000000 0.00000000 + x = -16.039069053 + -10.29166667 x = -16.039069053 + -10.29166667 Combine like terms: -16.039069053 + -10.29166667 = -26.330735723 x = -26.330735723 Simplifying x = -26.330735723Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.747402383, -26.330735723}
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