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Simplifying -2x2 + 4000x + -800000 = 0 Reorder the terms: -800000 + 4000x + -2x2 = 0 Solving -800000 + 4000x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-400000 + 2000x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-400000 + 2000x + -1x2)' equal to zero and attempt to solve: Simplifying -400000 + 2000x + -1x2 = 0 Solving -400000 + 2000x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 400000 + -2000x + x2 = 0 Move the constant term to the right: Add '-400000' to each side of the equation. 400000 + -2000x + -400000 + x2 = 0 + -400000 Reorder the terms: 400000 + -400000 + -2000x + x2 = 0 + -400000 Combine like terms: 400000 + -400000 = 0 0 + -2000x + x2 = 0 + -400000 -2000x + x2 = 0 + -400000 Combine like terms: 0 + -400000 = -400000 -2000x + x2 = -400000 The x term is -2000x. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000x + 1000000 + x2 = -400000 + 1000000 Reorder the terms: 1000000 + -2000x + x2 = -400000 + 1000000 Combine like terms: -400000 + 1000000 = 600000 1000000 + -2000x + x2 = 600000 Factor a perfect square on the left side: (x + -1000)(x + -1000) = 600000 Calculate the square root of the right side: 774.596669241 Break this problem into two subproblems by setting (x + -1000) equal to 774.596669241 and -774.596669241.Subproblem 1
x + -1000 = 774.596669241 Simplifying x + -1000 = 774.596669241 Reorder the terms: -1000 + x = 774.596669241 Solving -1000 + x = 774.596669241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = 774.596669241 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = 774.596669241 + 1000 x = 774.596669241 + 1000 Combine like terms: 774.596669241 + 1000 = 1774.596669241 x = 1774.596669241 Simplifying x = 1774.596669241Subproblem 2
x + -1000 = -774.596669241 Simplifying x + -1000 = -774.596669241 Reorder the terms: -1000 + x = -774.596669241 Solving -1000 + x = -774.596669241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = -774.596669241 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = -774.596669241 + 1000 x = -774.596669241 + 1000 Combine like terms: -774.596669241 + 1000 = 225.403330759 x = 225.403330759 Simplifying x = 225.403330759Solution
The solution to the problem is based on the solutions from the subproblems. x = {1774.596669241, 225.403330759}Solution
x = {1774.596669241, 225.403330759}
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