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Simplifying 10000x102 + -2500x101 + -125000x100 = 0 Reorder the terms: -125000x100 + -2500x101 + 10000x102 = 0 Solving -125000x100 + -2500x101 + 10000x102 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2500x100'. 2500x100(-50 + -1x + 4x2) = 0 Ignore the factor 2500.Subproblem 1
Set the factor 'x100' equal to zero and attempt to solve: Simplifying x100 = 0 Solving x100 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x100 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-50 + -1x + 4x2)' equal to zero and attempt to solve: Simplifying -50 + -1x + 4x2 = 0 Solving -50 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.5 + -0.25x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.25x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.25x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.25x + x2 = 0 + 12.5 -0.25x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.25x + x2 = 12.5 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 12.5 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 12.5 + 0.015625 Combine like terms: 12.5 + 0.015625 = 12.515625 0.015625 + -0.25x + x2 = 12.515625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 12.515625 Calculate the square root of the right side: 3.537742925 Break this problem into two subproblems by setting (x + -0.125) equal to 3.537742925 and -3.537742925.Subproblem 1
x + -0.125 = 3.537742925 Simplifying x + -0.125 = 3.537742925 Reorder the terms: -0.125 + x = 3.537742925 Solving -0.125 + x = 3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 3.537742925 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.537742925 + 0.125 x = 3.537742925 + 0.125 Combine like terms: 3.537742925 + 0.125 = 3.662742925 x = 3.662742925 Simplifying x = 3.662742925Subproblem 2
x + -0.125 = -3.537742925 Simplifying x + -0.125 = -3.537742925 Reorder the terms: -0.125 + x = -3.537742925 Solving -0.125 + x = -3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -3.537742925 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.537742925 + 0.125 x = -3.537742925 + 0.125 Combine like terms: -3.537742925 + 0.125 = -3.412742925 x = -3.412742925 Simplifying x = -3.412742925Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.662742925, -3.412742925}Solution
x = {3.662742925, -3.412742925}
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