408000000=340000x-0.061x^2

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Solution for 408000000=340000x-0.061x^2 equation:


Simplifying
408000000 = 340000x + -0.061x2

Solving
408000000 = 340000x + -0.061x2

Solving for variable 'x'.

Reorder the terms:
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 = 5572570.233468971

Subproblem 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 = 1200.258531029

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5572570.233468971, 1200.258531029}

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