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Simplifying 0.35x2 + -9x + -4000 = 0 Reorder the terms: -4000 + -9x + 0.35x2 = 0 Solving -4000 + -9x + 0.35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. -11428.57143 + -25.71428571x + x2 = 0 Move the constant term to the right: Add '11428.57143' to each side of the equation. -11428.57143 + -25.71428571x + 11428.57143 + x2 = 0 + 11428.57143 Reorder the terms: -11428.57143 + 11428.57143 + -25.71428571x + x2 = 0 + 11428.57143 Combine like terms: -11428.57143 + 11428.57143 = 0.00000 0.00000 + -25.71428571x + x2 = 0 + 11428.57143 -25.71428571x + x2 = 0 + 11428.57143 Combine like terms: 0 + 11428.57143 = 11428.57143 -25.71428571x + x2 = 11428.57143 The x term is -25.71428571x. Take half its coefficient (-12.85714286). Square it (165.3061225) and add it to both sides. Add '165.3061225' to each side of the equation. -25.71428571x + 165.3061225 + x2 = 11428.57143 + 165.3061225 Reorder the terms: 165.3061225 + -25.71428571x + x2 = 11428.57143 + 165.3061225 Combine like terms: 11428.57143 + 165.3061225 = 11593.8775525 165.3061225 + -25.71428571x + x2 = 11593.8775525 Factor a perfect square on the left side: (x + -12.85714286)(x + -12.85714286) = 11593.8775525 Calculate the square root of the right side: 107.674869642 Break this problem into two subproblems by setting (x + -12.85714286) equal to 107.674869642 and -107.674869642.Subproblem 1
x + -12.85714286 = 107.674869642 Simplifying x + -12.85714286 = 107.674869642 Reorder the terms: -12.85714286 + x = 107.674869642 Solving -12.85714286 + x = 107.674869642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.85714286' to each side of the equation. -12.85714286 + 12.85714286 + x = 107.674869642 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + x = 107.674869642 + 12.85714286 x = 107.674869642 + 12.85714286 Combine like terms: 107.674869642 + 12.85714286 = 120.532012502 x = 120.532012502 Simplifying x = 120.532012502Subproblem 2
x + -12.85714286 = -107.674869642 Simplifying x + -12.85714286 = -107.674869642 Reorder the terms: -12.85714286 + x = -107.674869642 Solving -12.85714286 + x = -107.674869642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.85714286' to each side of the equation. -12.85714286 + 12.85714286 + x = -107.674869642 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + x = -107.674869642 + 12.85714286 x = -107.674869642 + 12.85714286 Combine like terms: -107.674869642 + 12.85714286 = -94.817726782 x = -94.817726782 Simplifying x = -94.817726782Solution
The solution to the problem is based on the solutions from the subproblems. x = {120.532012502, -94.817726782}
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