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Simplifying 45000000x2 + 45450000x + -199955 = 0 Reorder the terms: -199955 + 45450000x + 45000000x2 = 0 Solving -199955 + 45450000x + 45000000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-39991 + 9090000x + 9000000x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-39991 + 9090000x + 9000000x2)' equal to zero and attempt to solve: Simplifying -39991 + 9090000x + 9000000x2 = 0 Solving -39991 + 9090000x + 9000000x2 = 0 Begin completing the square. Divide all terms by 9000000 the coefficient of the squared term: Divide each side by '9000000'. -0.004443444444 + 1.01x + x2 = 0.000000 Move the constant term to the right: Add '0.004443444444' to each side of the equation. -0.004443444444 + 1.01x + 0.004443444444 + x2 = 0.000000 + 0.004443444444 Reorder the terms: -0.004443444444 + 0.004443444444 + 1.01x + x2 = 0.000000 + 0.004443444444 Combine like terms: -0.004443444444 + 0.004443444444 = 0.000000000000 0.000000000000 + 1.01x + x2 = 0.000000 + 0.004443444444 1.01x + x2 = 0.000000 + 0.004443444444 Combine like terms: 0.000000 + 0.004443444444 = 0.004443444444 1.01x + x2 = 0.004443444444 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 = 0.004443444444 + 0.255025 Reorder the terms: 0.255025 + 1.01x + x2 = 0.004443444444 + 0.255025 Combine like terms: 0.004443444444 + 0.255025 = 0.259468444444 0.255025 + 1.01x + x2 = 0.259468444444 Factor a perfect square on the left side: (x + 0.505)(x + 0.505) = 0.259468444444 Calculate the square root of the right side: 0.509380452 Break this problem into two subproblems by setting (x + 0.505) equal to 0.509380452 and -0.509380452.Subproblem 1
x + 0.505 = 0.509380452 Simplifying x + 0.505 = 0.509380452 Reorder the terms: 0.505 + x = 0.509380452 Solving 0.505 + x = 0.509380452 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 = 0.509380452 + -0.505 Combine like terms: 0.505 + -0.505 = 0.000 0.000 + x = 0.509380452 + -0.505 x = 0.509380452 + -0.505 Combine like terms: 0.509380452 + -0.505 = 0.004380452 x = 0.004380452 Simplifying x = 0.004380452Subproblem 2
x + 0.505 = -0.509380452 Simplifying x + 0.505 = -0.509380452 Reorder the terms: 0.505 + x = -0.509380452 Solving 0.505 + x = -0.509380452 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 = -0.509380452 + -0.505 Combine like terms: 0.505 + -0.505 = 0.000 0.000 + x = -0.509380452 + -0.505 x = -0.509380452 + -0.505 Combine like terms: -0.509380452 + -0.505 = -1.014380452 x = -1.014380452 Simplifying x = -1.014380452Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.004380452, -1.014380452}Solution
x = {0.004380452, -1.014380452}
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