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Simplifying 800000 = -4x2 + 4000x Reorder the terms: 800000 = 4000x + -4x2 Solving 800000 = 4000x + -4x2 Solving for variable 'x'. Reorder the terms: 800000 + -4000x + 4x2 = 4000x + -4000x + -4x2 + 4x2 Combine like terms: 4000x + -4000x = 0 800000 + -4000x + 4x2 = 0 + -4x2 + 4x2 800000 + -4000x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 800000 + -4000x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(200000 + -1000x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(200000 + -1000x + x2)' equal to zero and attempt to solve: Simplifying 200000 + -1000x + x2 = 0 Solving 200000 + -1000x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200000' to each side of the equation. 200000 + -1000x + -200000 + x2 = 0 + -200000 Reorder the terms: 200000 + -200000 + -1000x + x2 = 0 + -200000 Combine like terms: 200000 + -200000 = 0 0 + -1000x + x2 = 0 + -200000 -1000x + x2 = 0 + -200000 Combine like terms: 0 + -200000 = -200000 -1000x + x2 = -200000 The x term is -1000x. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000x + 250000 + x2 = -200000 + 250000 Reorder the terms: 250000 + -1000x + x2 = -200000 + 250000 Combine like terms: -200000 + 250000 = 50000 250000 + -1000x + x2 = 50000 Factor a perfect square on the left side: (x + -500)(x + -500) = 50000 Calculate the square root of the right side: 223.60679775 Break this problem into two subproblems by setting (x + -500) equal to 223.60679775 and -223.60679775.Subproblem 1
x + -500 = 223.60679775 Simplifying x + -500 = 223.60679775 Reorder the terms: -500 + x = 223.60679775 Solving -500 + x = 223.60679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 223.60679775 + 500 Combine like terms: -500 + 500 = 0 0 + x = 223.60679775 + 500 x = 223.60679775 + 500 Combine like terms: 223.60679775 + 500 = 723.60679775 x = 723.60679775 Simplifying x = 723.60679775Subproblem 2
x + -500 = -223.60679775 Simplifying x + -500 = -223.60679775 Reorder the terms: -500 + x = -223.60679775 Solving -500 + x = -223.60679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -223.60679775 + 500 Combine like terms: -500 + 500 = 0 0 + x = -223.60679775 + 500 x = -223.60679775 + 500 Combine like terms: -223.60679775 + 500 = 276.39320225 x = 276.39320225 Simplifying x = 276.39320225Solution
The solution to the problem is based on the solutions from the subproblems. x = {723.60679775, 276.39320225}Solution
x = {723.60679775, 276.39320225}
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