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Simplifying 50 = -0.26x2 + -0.55x + 91.81 Reorder the terms: 50 = 91.81 + -0.55x + -0.26x2 Solving 50 = 91.81 + -0.55x + -0.26x2 Solving for variable 'x'. Combine like terms: 50 + -91.81 = -41.81 -41.81 + 0.55x + 0.26x2 = 91.81 + -0.55x + -0.26x2 + -91.81 + 0.55x + 0.26x2 Reorder the terms: -41.81 + 0.55x + 0.26x2 = 91.81 + -91.81 + -0.55x + 0.55x + -0.26x2 + 0.26x2 Combine like terms: 91.81 + -91.81 = 0.00 -41.81 + 0.55x + 0.26x2 = 0.00 + -0.55x + 0.55x + -0.26x2 + 0.26x2 -41.81 + 0.55x + 0.26x2 = -0.55x + 0.55x + -0.26x2 + 0.26x2 Combine like terms: -0.55x + 0.55x = 0.00 -41.81 + 0.55x + 0.26x2 = 0.00 + -0.26x2 + 0.26x2 -41.81 + 0.55x + 0.26x2 = -0.26x2 + 0.26x2 Combine like terms: -0.26x2 + 0.26x2 = 0.00 -41.81 + 0.55x + 0.26x2 = 0.00 Begin completing the square. Divide all terms by 0.26 the coefficient of the squared term: Divide each side by '0.26'. -160.8076923 + 2.115384615x + x2 = 0 Move the constant term to the right: Add '160.8076923' to each side of the equation. -160.8076923 + 2.115384615x + 160.8076923 + x2 = 0 + 160.8076923 Reorder the terms: -160.8076923 + 160.8076923 + 2.115384615x + x2 = 0 + 160.8076923 Combine like terms: -160.8076923 + 160.8076923 = 0.0000000 0.0000000 + 2.115384615x + x2 = 0 + 160.8076923 2.115384615x + x2 = 0 + 160.8076923 Combine like terms: 0 + 160.8076923 = 160.8076923 2.115384615x + x2 = 160.8076923 The x term is 2.115384615x. Take half its coefficient (1.057692308). Square it (1.118713018) and add it to both sides. Add '1.118713018' to each side of the equation. 2.115384615x + 1.118713018 + x2 = 160.8076923 + 1.118713018 Reorder the terms: 1.118713018 + 2.115384615x + x2 = 160.8076923 + 1.118713018 Combine like terms: 160.8076923 + 1.118713018 = 161.926405318 1.118713018 + 2.115384615x + x2 = 161.926405318 Factor a perfect square on the left side: (x + 1.057692308)(x + 1.057692308) = 161.926405318 Calculate the square root of the right side: 12.725030661 Break this problem into two subproblems by setting (x + 1.057692308) equal to 12.725030661 and -12.725030661.Subproblem 1
x + 1.057692308 = 12.725030661 Simplifying x + 1.057692308 = 12.725030661 Reorder the terms: 1.057692308 + x = 12.725030661 Solving 1.057692308 + x = 12.725030661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.057692308' to each side of the equation. 1.057692308 + -1.057692308 + x = 12.725030661 + -1.057692308 Combine like terms: 1.057692308 + -1.057692308 = 0.000000000 0.000000000 + x = 12.725030661 + -1.057692308 x = 12.725030661 + -1.057692308 Combine like terms: 12.725030661 + -1.057692308 = 11.667338353 x = 11.667338353 Simplifying x = 11.667338353Subproblem 2
x + 1.057692308 = -12.725030661 Simplifying x + 1.057692308 = -12.725030661 Reorder the terms: 1.057692308 + x = -12.725030661 Solving 1.057692308 + x = -12.725030661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.057692308' to each side of the equation. 1.057692308 + -1.057692308 + x = -12.725030661 + -1.057692308 Combine like terms: 1.057692308 + -1.057692308 = 0.000000000 0.000000000 + x = -12.725030661 + -1.057692308 x = -12.725030661 + -1.057692308 Combine like terms: -12.725030661 + -1.057692308 = -13.782722969 x = -13.782722969 Simplifying x = -13.782722969Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.667338353, -13.782722969}
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