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Simplifying 275000 = -425x2 + 45500x + -650000 Reorder the terms: 275000 = -650000 + 45500x + -425x2 Solving 275000 = -650000 + 45500x + -425x2 Solving for variable 'x'. Combine like terms: 275000 + 650000 = 925000 925000 + -45500x + 425x2 = -650000 + 45500x + -425x2 + 650000 + -45500x + 425x2 Reorder the terms: 925000 + -45500x + 425x2 = -650000 + 650000 + 45500x + -45500x + -425x2 + 425x2 Combine like terms: -650000 + 650000 = 0 925000 + -45500x + 425x2 = 0 + 45500x + -45500x + -425x2 + 425x2 925000 + -45500x + 425x2 = 45500x + -45500x + -425x2 + 425x2 Combine like terms: 45500x + -45500x = 0 925000 + -45500x + 425x2 = 0 + -425x2 + 425x2 925000 + -45500x + 425x2 = -425x2 + 425x2 Combine like terms: -425x2 + 425x2 = 0 925000 + -45500x + 425x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(37000 + -1820x + 17x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(37000 + -1820x + 17x2)' equal to zero and attempt to solve: Simplifying 37000 + -1820x + 17x2 = 0 Solving 37000 + -1820x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 2176.470588 + -107.0588235x + x2 = 0 Move the constant term to the right: Add '-2176.470588' to each side of the equation. 2176.470588 + -107.0588235x + -2176.470588 + x2 = 0 + -2176.470588 Reorder the terms: 2176.470588 + -2176.470588 + -107.0588235x + x2 = 0 + -2176.470588 Combine like terms: 2176.470588 + -2176.470588 = 0.000000 0.000000 + -107.0588235x + x2 = 0 + -2176.470588 -107.0588235x + x2 = 0 + -2176.470588 Combine like terms: 0 + -2176.470588 = -2176.470588 -107.0588235x + x2 = -2176.470588 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 = -2176.470588 + 2865.397922 Reorder the terms: 2865.397922 + -107.0588235x + x2 = -2176.470588 + 2865.397922 Combine like terms: -2176.470588 + 2865.397922 = 688.927334 2865.397922 + -107.0588235x + x2 = 688.927334 Factor a perfect square on the left side: (x + -53.52941175)(x + -53.52941175) = 688.927334 Calculate the square root of the right side: 26.247425283 Break this problem into two subproblems by setting (x + -53.52941175) equal to 26.247425283 and -26.247425283.Subproblem 1
x + -53.52941175 = 26.247425283 Simplifying x + -53.52941175 = 26.247425283 Reorder the terms: -53.52941175 + x = 26.247425283 Solving -53.52941175 + x = 26.247425283 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 = 26.247425283 + 53.52941175 Combine like terms: -53.52941175 + 53.52941175 = 0.00000000 0.00000000 + x = 26.247425283 + 53.52941175 x = 26.247425283 + 53.52941175 Combine like terms: 26.247425283 + 53.52941175 = 79.776837033 x = 79.776837033 Simplifying x = 79.776837033Subproblem 2
x + -53.52941175 = -26.247425283 Simplifying x + -53.52941175 = -26.247425283 Reorder the terms: -53.52941175 + x = -26.247425283 Solving -53.52941175 + x = -26.247425283 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 = -26.247425283 + 53.52941175 Combine like terms: -53.52941175 + 53.52941175 = 0.00000000 0.00000000 + x = -26.247425283 + 53.52941175 x = -26.247425283 + 53.52941175 Combine like terms: -26.247425283 + 53.52941175 = 27.281986467 x = 27.281986467 Simplifying x = 27.281986467Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.776837033, 27.281986467}Solution
x = {79.776837033, 27.281986467}
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