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Simplifying 250000 = -425x2 + 54500x + -650000 Reorder the terms: 250000 = -650000 + 54500x + -425x2 Solving 250000 = -650000 + 54500x + -425x2 Solving for variable 'x'. Combine like terms: 250000 + 650000 = 900000 900000 + -54500x + 425x2 = -650000 + 54500x + -425x2 + 650000 + -54500x + 425x2 Reorder the terms: 900000 + -54500x + 425x2 = -650000 + 650000 + 54500x + -54500x + -425x2 + 425x2 Combine like terms: -650000 + 650000 = 0 900000 + -54500x + 425x2 = 0 + 54500x + -54500x + -425x2 + 425x2 900000 + -54500x + 425x2 = 54500x + -54500x + -425x2 + 425x2 Combine like terms: 54500x + -54500x = 0 900000 + -54500x + 425x2 = 0 + -425x2 + 425x2 900000 + -54500x + 425x2 = -425x2 + 425x2 Combine like terms: -425x2 + 425x2 = 0 900000 + -54500x + 425x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(36000 + -2180x + 17x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(36000 + -2180x + 17x2)' equal to zero and attempt to solve: Simplifying 36000 + -2180x + 17x2 = 0 Solving 36000 + -2180x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 2117.647059 + -128.2352941x + x2 = 0 Move the constant term to the right: Add '-2117.647059' to each side of the equation. 2117.647059 + -128.2352941x + -2117.647059 + x2 = 0 + -2117.647059 Reorder the terms: 2117.647059 + -2117.647059 + -128.2352941x + x2 = 0 + -2117.647059 Combine like terms: 2117.647059 + -2117.647059 = 0.000000 0.000000 + -128.2352941x + x2 = 0 + -2117.647059 -128.2352941x + x2 = 0 + -2117.647059 Combine like terms: 0 + -2117.647059 = -2117.647059 -128.2352941x + x2 = -2117.647059 The x term is -128.2352941x. Take half its coefficient (-64.11764705). Square it (4111.072663) and add it to both sides. Add '4111.072663' to each side of the equation. -128.2352941x + 4111.072663 + x2 = -2117.647059 + 4111.072663 Reorder the terms: 4111.072663 + -128.2352941x + x2 = -2117.647059 + 4111.072663 Combine like terms: -2117.647059 + 4111.072663 = 1993.425604 4111.072663 + -128.2352941x + x2 = 1993.425604 Factor a perfect square on the left side: (x + -64.11764705)(x + -64.11764705) = 1993.425604 Calculate the square root of the right side: 44.647795063 Break this problem into two subproblems by setting (x + -64.11764705) equal to 44.647795063 and -44.647795063.Subproblem 1
x + -64.11764705 = 44.647795063 Simplifying x + -64.11764705 = 44.647795063 Reorder the terms: -64.11764705 + x = 44.647795063 Solving -64.11764705 + x = 44.647795063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '64.11764705' to each side of the equation. -64.11764705 + 64.11764705 + x = 44.647795063 + 64.11764705 Combine like terms: -64.11764705 + 64.11764705 = 0.00000000 0.00000000 + x = 44.647795063 + 64.11764705 x = 44.647795063 + 64.11764705 Combine like terms: 44.647795063 + 64.11764705 = 108.765442113 x = 108.765442113 Simplifying x = 108.765442113Subproblem 2
x + -64.11764705 = -44.647795063 Simplifying x + -64.11764705 = -44.647795063 Reorder the terms: -64.11764705 + x = -44.647795063 Solving -64.11764705 + x = -44.647795063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '64.11764705' to each side of the equation. -64.11764705 + 64.11764705 + x = -44.647795063 + 64.11764705 Combine like terms: -64.11764705 + 64.11764705 = 0.00000000 0.00000000 + x = -44.647795063 + 64.11764705 x = -44.647795063 + 64.11764705 Combine like terms: -44.647795063 + 64.11764705 = 19.469851987 x = 19.469851987 Simplifying x = 19.469851987Solution
The solution to the problem is based on the solutions from the subproblems. x = {108.765442113, 19.469851987}Solution
x = {108.765442113, 19.469851987}
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