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Simplifying x = -0.025x2 + 800x + 70000 Reorder the terms: x = 70000 + 800x + -0.025x2 Solving x = 70000 + 800x + -0.025x2 Solving for variable 'x'. Reorder the terms: -70000 + x + -800x + 0.025x2 = 70000 + 800x + -0.025x2 + -70000 + -800x + 0.025x2 Combine like terms: x + -800x = -799x -70000 + -799x + 0.025x2 = 70000 + 800x + -0.025x2 + -70000 + -800x + 0.025x2 Reorder the terms: -70000 + -799x + 0.025x2 = 70000 + -70000 + 800x + -800x + -0.025x2 + 0.025x2 Combine like terms: 70000 + -70000 = 0 -70000 + -799x + 0.025x2 = 0 + 800x + -800x + -0.025x2 + 0.025x2 -70000 + -799x + 0.025x2 = 800x + -800x + -0.025x2 + 0.025x2 Combine like terms: 800x + -800x = 0 -70000 + -799x + 0.025x2 = 0 + -0.025x2 + 0.025x2 -70000 + -799x + 0.025x2 = -0.025x2 + 0.025x2 Combine like terms: -0.025x2 + 0.025x2 = 0.000 -70000 + -799x + 0.025x2 = 0.000 Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. -2800000 + -31960x + x2 = 0 Move the constant term to the right: Add '2800000' to each side of the equation. -2800000 + -31960x + 2800000 + x2 = 0 + 2800000 Reorder the terms: -2800000 + 2800000 + -31960x + x2 = 0 + 2800000 Combine like terms: -2800000 + 2800000 = 0 0 + -31960x + x2 = 0 + 2800000 -31960x + x2 = 0 + 2800000 Combine like terms: 0 + 2800000 = 2800000 -31960x + x2 = 2800000 The x term is -31960x. Take half its coefficient (-15980). Square it (255360400) and add it to both sides. Add '255360400' to each side of the equation. -31960x + 255360400 + x2 = 2800000 + 255360400 Reorder the terms: 255360400 + -31960x + x2 = 2800000 + 255360400 Combine like terms: 2800000 + 255360400 = 258160400 255360400 + -31960x + x2 = 258160400 Factor a perfect square on the left side: (x + -15980)(x + -15980) = 258160400 Calculate the square root of the right side: 16067.370662308 Break this problem into two subproblems by setting (x + -15980) equal to 16067.370662308 and -16067.370662308.Subproblem 1
x + -15980 = 16067.370662308 Simplifying x + -15980 = 16067.370662308 Reorder the terms: -15980 + x = 16067.370662308 Solving -15980 + x = 16067.370662308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15980' to each side of the equation. -15980 + 15980 + x = 16067.370662308 + 15980 Combine like terms: -15980 + 15980 = 0 0 + x = 16067.370662308 + 15980 x = 16067.370662308 + 15980 Combine like terms: 16067.370662308 + 15980 = 32047.370662308 x = 32047.370662308 Simplifying x = 32047.370662308Subproblem 2
x + -15980 = -16067.370662308 Simplifying x + -15980 = -16067.370662308 Reorder the terms: -15980 + x = -16067.370662308 Solving -15980 + x = -16067.370662308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15980' to each side of the equation. -15980 + 15980 + x = -16067.370662308 + 15980 Combine like terms: -15980 + 15980 = 0 0 + x = -16067.370662308 + 15980 x = -16067.370662308 + 15980 Combine like terms: -16067.370662308 + 15980 = -87.370662308 x = -87.370662308 Simplifying x = -87.370662308Solution
The solution to the problem is based on the solutions from the subproblems. x = {32047.370662308, -87.370662308}
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