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Simplifying x = -56x2 + 800x + 30000 Reorder the terms: x = 30000 + 800x + -56x2 Solving x = 30000 + 800x + -56x2 Solving for variable 'x'. Reorder the terms: -30000 + x + -800x + 56x2 = 30000 + 800x + -56x2 + -30000 + -800x + 56x2 Combine like terms: x + -800x = -799x -30000 + -799x + 56x2 = 30000 + 800x + -56x2 + -30000 + -800x + 56x2 Reorder the terms: -30000 + -799x + 56x2 = 30000 + -30000 + 800x + -800x + -56x2 + 56x2 Combine like terms: 30000 + -30000 = 0 -30000 + -799x + 56x2 = 0 + 800x + -800x + -56x2 + 56x2 -30000 + -799x + 56x2 = 800x + -800x + -56x2 + 56x2 Combine like terms: 800x + -800x = 0 -30000 + -799x + 56x2 = 0 + -56x2 + 56x2 -30000 + -799x + 56x2 = -56x2 + 56x2 Combine like terms: -56x2 + 56x2 = 0 -30000 + -799x + 56x2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -535.7142857 + -14.26785714x + x2 = 0 Move the constant term to the right: Add '535.7142857' to each side of the equation. -535.7142857 + -14.26785714x + 535.7142857 + x2 = 0 + 535.7142857 Reorder the terms: -535.7142857 + 535.7142857 + -14.26785714x + x2 = 0 + 535.7142857 Combine like terms: -535.7142857 + 535.7142857 = 0.0000000 0.0000000 + -14.26785714x + x2 = 0 + 535.7142857 -14.26785714x + x2 = 0 + 535.7142857 Combine like terms: 0 + 535.7142857 = 535.7142857 -14.26785714x + x2 = 535.7142857 The x term is -14.26785714x. Take half its coefficient (-7.13392857). Square it (50.89293684) and add it to both sides. Add '50.89293684' to each side of the equation. -14.26785714x + 50.89293684 + x2 = 535.7142857 + 50.89293684 Reorder the terms: 50.89293684 + -14.26785714x + x2 = 535.7142857 + 50.89293684 Combine like terms: 535.7142857 + 50.89293684 = 586.60722254 50.89293684 + -14.26785714x + x2 = 586.60722254 Factor a perfect square on the left side: (x + -7.13392857)(x + -7.13392857) = 586.60722254 Calculate the square root of the right side: 24.219975692 Break this problem into two subproblems by setting (x + -7.13392857) equal to 24.219975692 and -24.219975692.Subproblem 1
x + -7.13392857 = 24.219975692 Simplifying x + -7.13392857 = 24.219975692 Reorder the terms: -7.13392857 + x = 24.219975692 Solving -7.13392857 + x = 24.219975692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.13392857' to each side of the equation. -7.13392857 + 7.13392857 + x = 24.219975692 + 7.13392857 Combine like terms: -7.13392857 + 7.13392857 = 0.00000000 0.00000000 + x = 24.219975692 + 7.13392857 x = 24.219975692 + 7.13392857 Combine like terms: 24.219975692 + 7.13392857 = 31.353904262 x = 31.353904262 Simplifying x = 31.353904262Subproblem 2
x + -7.13392857 = -24.219975692 Simplifying x + -7.13392857 = -24.219975692 Reorder the terms: -7.13392857 + x = -24.219975692 Solving -7.13392857 + x = -24.219975692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.13392857' to each side of the equation. -7.13392857 + 7.13392857 + x = -24.219975692 + 7.13392857 Combine like terms: -7.13392857 + 7.13392857 = 0.00000000 0.00000000 + x = -24.219975692 + 7.13392857 x = -24.219975692 + 7.13392857 Combine like terms: -24.219975692 + 7.13392857 = -17.086047122 x = -17.086047122 Simplifying x = -17.086047122Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.353904262, -17.086047122}
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