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Simplifying 650 = 11.5x + -0.05x2 Solving 650 = 11.5x + -0.05x2 Solving for variable 'x'. Reorder the terms: 650 + -11.5x + 0.05x2 = 11.5x + -11.5x + -0.05x2 + 0.05x2 Combine like terms: 11.5x + -11.5x = 0.0 650 + -11.5x + 0.05x2 = 0.0 + -0.05x2 + 0.05x2 650 + -11.5x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 650 + -11.5x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 13000 + -230x + x2 = 0 Move the constant term to the right: Add '-13000' to each side of the equation. 13000 + -230x + -13000 + x2 = 0 + -13000 Reorder the terms: 13000 + -13000 + -230x + x2 = 0 + -13000 Combine like terms: 13000 + -13000 = 0 0 + -230x + x2 = 0 + -13000 -230x + x2 = 0 + -13000 Combine like terms: 0 + -13000 = -13000 -230x + x2 = -13000 The x term is -230x. Take half its coefficient (-115). Square it (13225) and add it to both sides. Add '13225' to each side of the equation. -230x + 13225 + x2 = -13000 + 13225 Reorder the terms: 13225 + -230x + x2 = -13000 + 13225 Combine like terms: -13000 + 13225 = 225 13225 + -230x + x2 = 225 Factor a perfect square on the left side: (x + -115)(x + -115) = 225 Calculate the square root of the right side: 15 Break this problem into two subproblems by setting (x + -115) equal to 15 and -15.Subproblem 1
x + -115 = 15 Simplifying x + -115 = 15 Reorder the terms: -115 + x = 15 Solving -115 + x = 15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '115' to each side of the equation. -115 + 115 + x = 15 + 115 Combine like terms: -115 + 115 = 0 0 + x = 15 + 115 x = 15 + 115 Combine like terms: 15 + 115 = 130 x = 130 Simplifying x = 130Subproblem 2
x + -115 = -15 Simplifying x + -115 = -15 Reorder the terms: -115 + x = -15 Solving -115 + x = -15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '115' to each side of the equation. -115 + 115 + x = -15 + 115 Combine like terms: -115 + 115 = 0 0 + x = -15 + 115 x = -15 + 115 Combine like terms: -15 + 115 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {130, 100}
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