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Simplifying 2000 + 4x + -12x2 = 0 Solving 2000 + 4x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(500 + x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(500 + x + -3x2)' equal to zero and attempt to solve: Simplifying 500 + x + -3x2 = 0 Solving 500 + x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -166.6666667 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + -0.3333333333x + 166.6666667 + x2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + -0.3333333333x + x2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + -0.3333333333x + x2 = 0 + 166.6666667 -0.3333333333x + x2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 -0.3333333333x + x2 = 166.6666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.3333333333x + 0.25 + x2 = 166.6666667 + 0.25 Reorder the terms: 0.25 + -0.3333333333x + x2 = 166.6666667 + 0.25 Combine like terms: 166.6666667 + 0.25 = 166.9166667 0.25 + -0.3333333333x + x2 = 166.9166667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 166.9166667 Calculate the square root of the right side: 12.919623319 Break this problem into two subproblems by setting (x + 0.5) equal to 12.919623319 and -12.919623319.Subproblem 1
x + 0.5 = 12.919623319 Simplifying x + 0.5 = 12.919623319 Reorder the terms: 0.5 + x = 12.919623319 Solving 0.5 + x = 12.919623319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 12.919623319 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.919623319 + -0.5 x = 12.919623319 + -0.5 Combine like terms: 12.919623319 + -0.5 = 12.419623319 x = 12.419623319 Simplifying x = 12.419623319Subproblem 2
x + 0.5 = -12.919623319 Simplifying x + 0.5 = -12.919623319 Reorder the terms: 0.5 + x = -12.919623319 Solving 0.5 + x = -12.919623319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -12.919623319 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.919623319 + -0.5 x = -12.919623319 + -0.5 Combine like terms: -12.919623319 + -0.5 = -13.419623319 x = -13.419623319 Simplifying x = -13.419623319Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.419623319, -13.419623319}Solution
x = {12.419623319, -13.419623319}
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