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Simplifying 14000 = 0.125x2 + 20x + 5000 Reorder the terms: 14000 = 5000 + 20x + 0.125x2 Solving 14000 = 5000 + 20x + 0.125x2 Solving for variable 'x'. Combine like terms: 14000 + -5000 = 9000 9000 + -20x + -0.125x2 = 5000 + 20x + 0.125x2 + -5000 + -20x + -0.125x2 Reorder the terms: 9000 + -20x + -0.125x2 = 5000 + -5000 + 20x + -20x + 0.125x2 + -0.125x2 Combine like terms: 5000 + -5000 = 0 9000 + -20x + -0.125x2 = 0 + 20x + -20x + 0.125x2 + -0.125x2 9000 + -20x + -0.125x2 = 20x + -20x + 0.125x2 + -0.125x2 Combine like terms: 20x + -20x = 0 9000 + -20x + -0.125x2 = 0 + 0.125x2 + -0.125x2 9000 + -20x + -0.125x2 = 0.125x2 + -0.125x2 Combine like terms: 0.125x2 + -0.125x2 = 0.000 9000 + -20x + -0.125x2 = 0.000 Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. -72000 + 160x + x2 = 0 Move the constant term to the right: Add '72000' to each side of the equation. -72000 + 160x + 72000 + x2 = 0 + 72000 Reorder the terms: -72000 + 72000 + 160x + x2 = 0 + 72000 Combine like terms: -72000 + 72000 = 0 0 + 160x + x2 = 0 + 72000 160x + x2 = 0 + 72000 Combine like terms: 0 + 72000 = 72000 160x + x2 = 72000 The x term is 160x. Take half its coefficient (80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. 160x + 6400 + x2 = 72000 + 6400 Reorder the terms: 6400 + 160x + x2 = 72000 + 6400 Combine like terms: 72000 + 6400 = 78400 6400 + 160x + x2 = 78400 Factor a perfect square on the left side: (x + 80)(x + 80) = 78400 Calculate the square root of the right side: 280 Break this problem into two subproblems by setting (x + 80) equal to 280 and -280.Subproblem 1
x + 80 = 280 Simplifying x + 80 = 280 Reorder the terms: 80 + x = 280 Solving 80 + x = 280 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = 280 + -80 Combine like terms: 80 + -80 = 0 0 + x = 280 + -80 x = 280 + -80 Combine like terms: 280 + -80 = 200 x = 200 Simplifying x = 200Subproblem 2
x + 80 = -280 Simplifying x + 80 = -280 Reorder the terms: 80 + x = -280 Solving 80 + x = -280 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = -280 + -80 Combine like terms: 80 + -80 = 0 0 + x = -280 + -80 x = -280 + -80 Combine like terms: -280 + -80 = -360 x = -360 Simplifying x = -360Solution
The solution to the problem is based on the solutions from the subproblems. x = {200, -360}
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