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Simplifying 45000000x2 + 45450000x + -19550000 = 0 Reorder the terms: -19550000 + 45450000x + 45000000x2 = 0 Solving -19550000 + 45450000x + 45000000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50000'. 50000(-391 + 909x + 900x2) = 0 Ignore the factor 50000.Subproblem 1
Set the factor '(-391 + 909x + 900x2)' equal to zero and attempt to solve: Simplifying -391 + 909x + 900x2 = 0 Solving -391 + 909x + 900x2 = 0 Begin completing the square. Divide all terms by 900 the coefficient of the squared term: Divide each side by '900'. -0.4344444444 + 1.01x + x2 = 0.00 Move the constant term to the right: Add '0.4344444444' to each side of the equation. -0.4344444444 + 1.01x + 0.4344444444 + x2 = 0.00 + 0.4344444444 Reorder the terms: -0.4344444444 + 0.4344444444 + 1.01x + x2 = 0.00 + 0.4344444444 Combine like terms: -0.4344444444 + 0.4344444444 = 0.0000000000 0.0000000000 + 1.01x + x2 = 0.00 + 0.4344444444 1.01x + x2 = 0.00 + 0.4344444444 Combine like terms: 0.00 + 0.4344444444 = 0.4344444444 1.01x + x2 = 0.4344444444 The x term is 1.01x. Take half its coefficient (0.505). Square it (0.255025) and add it to both sides. Add '0.255025' to each side of the equation. 1.01x + 0.255025 + x2 = 0.4344444444 + 0.255025 Reorder the terms: 0.255025 + 1.01x + x2 = 0.4344444444 + 0.255025 Combine like terms: 0.4344444444 + 0.255025 = 0.6894694444 0.255025 + 1.01x + x2 = 0.6894694444 Factor a perfect square on the left side: (x + 0.505)(x + 0.505) = 0.6894694444 Calculate the square root of the right side: 0.830342968 Break this problem into two subproblems by setting (x + 0.505) equal to 0.830342968 and -0.830342968.Subproblem 1
x + 0.505 = 0.830342968 Simplifying x + 0.505 = 0.830342968 Reorder the terms: 0.505 + x = 0.830342968 Solving 0.505 + x = 0.830342968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.505' to each side of the equation. 0.505 + -0.505 + x = 0.830342968 + -0.505 Combine like terms: 0.505 + -0.505 = 0.000 0.000 + x = 0.830342968 + -0.505 x = 0.830342968 + -0.505 Combine like terms: 0.830342968 + -0.505 = 0.325342968 x = 0.325342968 Simplifying x = 0.325342968Subproblem 2
x + 0.505 = -0.830342968 Simplifying x + 0.505 = -0.830342968 Reorder the terms: 0.505 + x = -0.830342968 Solving 0.505 + x = -0.830342968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.505' to each side of the equation. 0.505 + -0.505 + x = -0.830342968 + -0.505 Combine like terms: 0.505 + -0.505 = 0.000 0.000 + x = -0.830342968 + -0.505 x = -0.830342968 + -0.505 Combine like terms: -0.830342968 + -0.505 = -1.335342968 x = -1.335342968 Simplifying x = -1.335342968Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.325342968, -1.335342968}Solution
x = {0.325342968, -1.335342968}
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