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Simplifying 18x(x) + -6000x + -150000 = 0 Multiply x * x 18x2 + -6000x + -150000 = 0 Reorder the terms: -150000 + -6000x + 18x2 = 0 Solving -150000 + -6000x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-25000 + -1000x + 3x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-25000 + -1000x + 3x2)' equal to zero and attempt to solve: Simplifying -25000 + -1000x + 3x2 = 0 Solving -25000 + -1000x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8333.333333 + -333.3333333x + x2 = 0 Move the constant term to the right: Add '8333.333333' to each side of the equation. -8333.333333 + -333.3333333x + 8333.333333 + x2 = 0 + 8333.333333 Reorder the terms: -8333.333333 + 8333.333333 + -333.3333333x + x2 = 0 + 8333.333333 Combine like terms: -8333.333333 + 8333.333333 = 0.000000 0.000000 + -333.3333333x + x2 = 0 + 8333.333333 -333.3333333x + x2 = 0 + 8333.333333 Combine like terms: 0 + 8333.333333 = 8333.333333 -333.3333333x + x2 = 8333.333333 The x term is -333.3333333x. Take half its coefficient (-166.6666667). Square it (27777.77779) and add it to both sides. Add '27777.77779' to each side of the equation. -333.3333333x + 27777.77779 + x2 = 8333.333333 + 27777.77779 Reorder the terms: 27777.77779 + -333.3333333x + x2 = 8333.333333 + 27777.77779 Combine like terms: 8333.333333 + 27777.77779 = 36111.111123 27777.77779 + -333.3333333x + x2 = 36111.111123 Factor a perfect square on the left side: (x + -166.6666667)(x + -166.6666667) = 36111.111123 Calculate the square root of the right side: 190.029237548 Break this problem into two subproblems by setting (x + -166.6666667) equal to 190.029237548 and -190.029237548.Subproblem 1
x + -166.6666667 = 190.029237548 Simplifying x + -166.6666667 = 190.029237548 Reorder the terms: -166.6666667 + x = 190.029237548 Solving -166.6666667 + x = 190.029237548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.6666667' to each side of the equation. -166.6666667 + 166.6666667 + x = 190.029237548 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + x = 190.029237548 + 166.6666667 x = 190.029237548 + 166.6666667 Combine like terms: 190.029237548 + 166.6666667 = 356.695904248 x = 356.695904248 Simplifying x = 356.695904248Subproblem 2
x + -166.6666667 = -190.029237548 Simplifying x + -166.6666667 = -190.029237548 Reorder the terms: -166.6666667 + x = -190.029237548 Solving -166.6666667 + x = -190.029237548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.6666667' to each side of the equation. -166.6666667 + 166.6666667 + x = -190.029237548 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + x = -190.029237548 + 166.6666667 x = -190.029237548 + 166.6666667 Combine like terms: -190.029237548 + 166.6666667 = -23.362570848 x = -23.362570848 Simplifying x = -23.362570848Solution
The solution to the problem is based on the solutions from the subproblems. x = {356.695904248, -23.362570848}Solution
x = {356.695904248, -23.362570848}
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