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Simplifying 250000 = -425x2 + 45500x + -650000 Reorder the terms: 250000 = -650000 + 45500x + -425x2 Solving 250000 = -650000 + 45500x + -425x2 Solving for variable 'x'. Combine like terms: 250000 + 650000 = 900000 900000 + -45500x + 425x2 = -650000 + 45500x + -425x2 + 650000 + -45500x + 425x2 Reorder the terms: 900000 + -45500x + 425x2 = -650000 + 650000 + 45500x + -45500x + -425x2 + 425x2 Combine like terms: -650000 + 650000 = 0 900000 + -45500x + 425x2 = 0 + 45500x + -45500x + -425x2 + 425x2 900000 + -45500x + 425x2 = 45500x + -45500x + -425x2 + 425x2 Combine like terms: 45500x + -45500x = 0 900000 + -45500x + 425x2 = 0 + -425x2 + 425x2 900000 + -45500x + 425x2 = -425x2 + 425x2 Combine like terms: -425x2 + 425x2 = 0 900000 + -45500x + 425x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(36000 + -1820x + 17x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(36000 + -1820x + 17x2)' equal to zero and attempt to solve: Simplifying 36000 + -1820x + 17x2 = 0 Solving 36000 + -1820x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 2117.647059 + -107.0588235x + x2 = 0 Move the constant term to the right: Add '-2117.647059' to each side of the equation. 2117.647059 + -107.0588235x + -2117.647059 + x2 = 0 + -2117.647059 Reorder the terms: 2117.647059 + -2117.647059 + -107.0588235x + x2 = 0 + -2117.647059 Combine like terms: 2117.647059 + -2117.647059 = 0.000000 0.000000 + -107.0588235x + x2 = 0 + -2117.647059 -107.0588235x + x2 = 0 + -2117.647059 Combine like terms: 0 + -2117.647059 = -2117.647059 -107.0588235x + x2 = -2117.647059 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 = -2117.647059 + 2865.397922 Reorder the terms: 2865.397922 + -107.0588235x + x2 = -2117.647059 + 2865.397922 Combine like terms: -2117.647059 + 2865.397922 = 747.750863 2865.397922 + -107.0588235x + x2 = 747.750863 Factor a perfect square on the left side: (x + -53.52941175)(x + -53.52941175) = 747.750863 Calculate the square root of the right side: 27.345033608 Break this problem into two subproblems by setting (x + -53.52941175) equal to 27.345033608 and -27.345033608.Subproblem 1
x + -53.52941175 = 27.345033608 Simplifying x + -53.52941175 = 27.345033608 Reorder the terms: -53.52941175 + x = 27.345033608 Solving -53.52941175 + x = 27.345033608 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 = 27.345033608 + 53.52941175 Combine like terms: -53.52941175 + 53.52941175 = 0.00000000 0.00000000 + x = 27.345033608 + 53.52941175 x = 27.345033608 + 53.52941175 Combine like terms: 27.345033608 + 53.52941175 = 80.874445358 x = 80.874445358 Simplifying x = 80.874445358Subproblem 2
x + -53.52941175 = -27.345033608 Simplifying x + -53.52941175 = -27.345033608 Reorder the terms: -53.52941175 + x = -27.345033608 Solving -53.52941175 + x = -27.345033608 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 = -27.345033608 + 53.52941175 Combine like terms: -53.52941175 + 53.52941175 = 0.00000000 0.00000000 + x = -27.345033608 + 53.52941175 x = -27.345033608 + 53.52941175 Combine like terms: -27.345033608 + 53.52941175 = 26.184378142 x = 26.184378142 Simplifying x = 26.184378142Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.874445358, 26.184378142}Solution
x = {80.874445358, 26.184378142}
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