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Simplifying 450 = -425x2 + 4500x + -650000 Reorder the terms: 450 = -650000 + 4500x + -425x2 Solving 450 = -650000 + 4500x + -425x2 Solving for variable 'x'. Combine like terms: 450 + 650000 = 650450 650450 + -4500x + 425x2 = -650000 + 4500x + -425x2 + 650000 + -4500x + 425x2 Reorder the terms: 650450 + -4500x + 425x2 = -650000 + 650000 + 4500x + -4500x + -425x2 + 425x2 Combine like terms: -650000 + 650000 = 0 650450 + -4500x + 425x2 = 0 + 4500x + -4500x + -425x2 + 425x2 650450 + -4500x + 425x2 = 4500x + -4500x + -425x2 + 425x2 Combine like terms: 4500x + -4500x = 0 650450 + -4500x + 425x2 = 0 + -425x2 + 425x2 650450 + -4500x + 425x2 = -425x2 + 425x2 Combine like terms: -425x2 + 425x2 = 0 650450 + -4500x + 425x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(26018 + -180x + 17x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(26018 + -180x + 17x2)' equal to zero and attempt to solve: Simplifying 26018 + -180x + 17x2 = 0 Solving 26018 + -180x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 1530.470588 + -10.58823529x + x2 = 0 Move the constant term to the right: Add '-1530.470588' to each side of the equation. 1530.470588 + -10.58823529x + -1530.470588 + x2 = 0 + -1530.470588 Reorder the terms: 1530.470588 + -1530.470588 + -10.58823529x + x2 = 0 + -1530.470588 Combine like terms: 1530.470588 + -1530.470588 = 0.000000 0.000000 + -10.58823529x + x2 = 0 + -1530.470588 -10.58823529x + x2 = 0 + -1530.470588 Combine like terms: 0 + -1530.470588 = -1530.470588 -10.58823529x + x2 = -1530.470588 The x term is -10.58823529x. Take half its coefficient (-5.294117645). Square it (28.02768164) and add it to both sides. Add '28.02768164' to each side of the equation. -10.58823529x + 28.02768164 + x2 = -1530.470588 + 28.02768164 Reorder the terms: 28.02768164 + -10.58823529x + x2 = -1530.470588 + 28.02768164 Combine like terms: -1530.470588 + 28.02768164 = -1502.44290636 28.02768164 + -10.58823529x + x2 = -1502.44290636 Factor a perfect square on the left side: (x + -5.294117645)(x + -5.294117645) = -1502.44290636 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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