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Simplifying 0 = 340000x + -0.061x2 + -408000000 Reorder the terms: 0 = -408000000 + 340000x + -0.061x2 Solving 0 = -408000000 + 340000x + -0.061x2 Solving for variable 'x'. Combine like terms: 0 + 408000000 = 408000000 408000000 + -340000x + 0.061x2 = -408000000 + 340000x + -0.061x2 + 408000000 + -340000x + 0.061x2 Reorder the terms: 408000000 + -340000x + 0.061x2 = -408000000 + 408000000 + 340000x + -340000x + -0.061x2 + 0.061x2 Combine like terms: -408000000 + 408000000 = 0 408000000 + -340000x + 0.061x2 = 0 + 340000x + -340000x + -0.061x2 + 0.061x2 408000000 + -340000x + 0.061x2 = 340000x + -340000x + -0.061x2 + 0.061x2 Combine like terms: 340000x + -340000x = 0 408000000 + -340000x + 0.061x2 = 0 + -0.061x2 + 0.061x2 408000000 + -340000x + 0.061x2 = -0.061x2 + 0.061x2 Combine like terms: -0.061x2 + 0.061x2 = 0.000 408000000 + -340000x + 0.061x2 = 0.000 Begin completing the square. Divide all terms by 0.061 the coefficient of the squared term: Divide each side by '0.061'. 6688524590 + -5573770.492x + x2 = 0 Move the constant term to the right: Add '-6688524590' to each side of the equation. 6688524590 + -5573770.492x + -6688524590 + x2 = 0 + -6688524590 Reorder the terms: 6688524590 + -6688524590 + -5573770.492x + x2 = 0 + -6688524590 Combine like terms: 6688524590 + -6688524590 = 0 0 + -5573770.492x + x2 = 0 + -6688524590 -5573770.492x + x2 = 0 + -6688524590 Combine like terms: 0 + -6688524590 = -6688524590 -5573770.492x + x2 = -6688524590 The x term is -5573770.492x. Take half its coefficient (-2786885.246). Square it (7766729374000) and add it to both sides. Add '7766729374000' to each side of the equation. -5573770.492x + 7766729374000 + x2 = -6688524590 + 7766729374000 Reorder the terms: 7766729374000 + -5573770.492x + x2 = -6688524590 + 7766729374000 Combine like terms: -6688524590 + 7766729374000 = 7760040849410 7766729374000 + -5573770.492x + x2 = 7760040849410 Factor a perfect square on the left side: (x + -2786885.246)(x + -2786885.246) = 7760040849410 Calculate the square root of the right side: 2785684.987468971 Break this problem into two subproblems by setting (x + -2786885.246) equal to 2785684.987468971 and -2785684.987468971.Subproblem 1
x + -2786885.246 = 2785684.987468971 Simplifying x + -2786885.246 = 2785684.987468971 Reorder the terms: -2786885.246 + x = 2785684.987468971 Solving -2786885.246 + x = 2785684.987468971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2786885.246' to each side of the equation. -2786885.246 + 2786885.246 + x = 2785684.987468971 + 2786885.246 Combine like terms: -2786885.246 + 2786885.246 = 0.000 0.000 + x = 2785684.987468971 + 2786885.246 x = 2785684.987468971 + 2786885.246 Combine like terms: 2785684.987468971 + 2786885.246 = 5572570.233468971 x = 5572570.233468971 Simplifying x = 5572570.233468971Subproblem 2
x + -2786885.246 = -2785684.987468971 Simplifying x + -2786885.246 = -2785684.987468971 Reorder the terms: -2786885.246 + x = -2785684.987468971 Solving -2786885.246 + x = -2785684.987468971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2786885.246' to each side of the equation. -2786885.246 + 2786885.246 + x = -2785684.987468971 + 2786885.246 Combine like terms: -2786885.246 + 2786885.246 = 0.000 0.000 + x = -2785684.987468971 + 2786885.246 x = -2785684.987468971 + 2786885.246 Combine like terms: -2785684.987468971 + 2786885.246 = 1200.258531029 x = 1200.258531029 Simplifying x = 1200.258531029Solution
The solution to the problem is based on the solutions from the subproblems. x = {5572570.233468971, 1200.258531029}
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