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Simplifying 450000 = -425x2 + 45500x + -650000 Reorder the terms: 450000 = -650000 + 45500x + -425x2 Solving 450000 = -650000 + 45500x + -425x2 Solving for variable 'x'. Combine like terms: 450000 + 650000 = 1100000 1100000 + -45500x + 425x2 = -650000 + 45500x + -425x2 + 650000 + -45500x + 425x2 Reorder the terms: 1100000 + -45500x + 425x2 = -650000 + 650000 + 45500x + -45500x + -425x2 + 425x2 Combine like terms: -650000 + 650000 = 0 1100000 + -45500x + 425x2 = 0 + 45500x + -45500x + -425x2 + 425x2 1100000 + -45500x + 425x2 = 45500x + -45500x + -425x2 + 425x2 Combine like terms: 45500x + -45500x = 0 1100000 + -45500x + 425x2 = 0 + -425x2 + 425x2 1100000 + -45500x + 425x2 = -425x2 + 425x2 Combine like terms: -425x2 + 425x2 = 0 1100000 + -45500x + 425x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(44000 + -1820x + 17x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(44000 + -1820x + 17x2)' equal to zero and attempt to solve: Simplifying 44000 + -1820x + 17x2 = 0 Solving 44000 + -1820x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 2588.235294 + -107.0588235x + x2 = 0 Move the constant term to the right: Add '-2588.235294' to each side of the equation. 2588.235294 + -107.0588235x + -2588.235294 + x2 = 0 + -2588.235294 Reorder the terms: 2588.235294 + -2588.235294 + -107.0588235x + x2 = 0 + -2588.235294 Combine like terms: 2588.235294 + -2588.235294 = 0.000000 0.000000 + -107.0588235x + x2 = 0 + -2588.235294 -107.0588235x + x2 = 0 + -2588.235294 Combine like terms: 0 + -2588.235294 = -2588.235294 -107.0588235x + x2 = -2588.235294 The x term is -107.0588235x. Take half its coefficient (-53.52941175). Square it (2865.397922) and add it to both sides. Add '2865.397922' to each side of the equation. -107.0588235x + 2865.397922 + x2 = -2588.235294 + 2865.397922 Reorder the terms: 2865.397922 + -107.0588235x + x2 = -2588.235294 + 2865.397922 Combine like terms: -2588.235294 + 2865.397922 = 277.162628 2865.397922 + -107.0588235x + x2 = 277.162628 Factor a perfect square on the left side: (x + -53.52941175)(x + -53.52941175) = 277.162628 Calculate the square root of the right side: 16.648201945 Break this problem into two subproblems by setting (x + -53.52941175) equal to 16.648201945 and -16.648201945.Subproblem 1
x + -53.52941175 = 16.648201945 Simplifying x + -53.52941175 = 16.648201945 Reorder the terms: -53.52941175 + x = 16.648201945 Solving -53.52941175 + x = 16.648201945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53.52941175' to each side of the equation. -53.52941175 + 53.52941175 + x = 16.648201945 + 53.52941175 Combine like terms: -53.52941175 + 53.52941175 = 0.00000000 0.00000000 + x = 16.648201945 + 53.52941175 x = 16.648201945 + 53.52941175 Combine like terms: 16.648201945 + 53.52941175 = 70.177613695 x = 70.177613695 Simplifying x = 70.177613695Subproblem 2
x + -53.52941175 = -16.648201945 Simplifying x + -53.52941175 = -16.648201945 Reorder the terms: -53.52941175 + x = -16.648201945 Solving -53.52941175 + x = -16.648201945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53.52941175' to each side of the equation. -53.52941175 + 53.52941175 + x = -16.648201945 + 53.52941175 Combine like terms: -53.52941175 + 53.52941175 = 0.00000000 0.00000000 + x = -16.648201945 + 53.52941175 x = -16.648201945 + 53.52941175 Combine like terms: -16.648201945 + 53.52941175 = 36.881209805 x = 36.881209805 Simplifying x = 36.881209805Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.177613695, 36.881209805}Solution
x = {70.177613695, 36.881209805}
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