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Simplifying 0 = 419650x2 + -419650x + -4000000 Reorder the terms: 0 = -4000000 + -419650x + 419650x2 Solving 0 = -4000000 + -419650x + 419650x2 Solving for variable 'x'. Combine like terms: 0 + 4000000 = 4000000 4000000 + 419650x + -419650x2 = -4000000 + -419650x + 419650x2 + 4000000 + 419650x + -419650x2 Reorder the terms: 4000000 + 419650x + -419650x2 = -4000000 + 4000000 + -419650x + 419650x + 419650x2 + -419650x2 Combine like terms: -4000000 + 4000000 = 0 4000000 + 419650x + -419650x2 = 0 + -419650x + 419650x + 419650x2 + -419650x2 4000000 + 419650x + -419650x2 = -419650x + 419650x + 419650x2 + -419650x2 Combine like terms: -419650x + 419650x = 0 4000000 + 419650x + -419650x2 = 0 + 419650x2 + -419650x2 4000000 + 419650x + -419650x2 = 419650x2 + -419650x2 Combine like terms: 419650x2 + -419650x2 = 0 4000000 + 419650x + -419650x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(80000 + 8393x + -8393x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(80000 + 8393x + -8393x2)' equal to zero and attempt to solve: Simplifying 80000 + 8393x + -8393x2 = 0 Solving 80000 + 8393x + -8393x2 = 0 Begin completing the square. Divide all terms by -8393 the coefficient of the squared term: Divide each side by '-8393'. -9.531752651 + -1x + x2 = 0 Move the constant term to the right: Add '9.531752651' to each side of the equation. -9.531752651 + -1x + 9.531752651 + x2 = 0 + 9.531752651 Reorder the terms: -9.531752651 + 9.531752651 + -1x + x2 = 0 + 9.531752651 Combine like terms: -9.531752651 + 9.531752651 = 0.000000000 0.000000000 + -1x + x2 = 0 + 9.531752651 -1x + x2 = 0 + 9.531752651 Combine like terms: 0 + 9.531752651 = 9.531752651 -1x + x2 = 9.531752651 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 9.531752651 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 9.531752651 + 0.25 Combine like terms: 9.531752651 + 0.25 = 9.781752651 0.25 + -1x + x2 = 9.781752651 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 9.781752651 Calculate the square root of the right side: 3.12757936 Break this problem into two subproblems by setting (x + -0.5) equal to 3.12757936 and -3.12757936.Subproblem 1
x + -0.5 = 3.12757936 Simplifying x + -0.5 = 3.12757936 Reorder the terms: -0.5 + x = 3.12757936 Solving -0.5 + x = 3.12757936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.12757936 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.12757936 + 0.5 x = 3.12757936 + 0.5 Combine like terms: 3.12757936 + 0.5 = 3.62757936 x = 3.62757936 Simplifying x = 3.62757936Subproblem 2
x + -0.5 = -3.12757936 Simplifying x + -0.5 = -3.12757936 Reorder the terms: -0.5 + x = -3.12757936 Solving -0.5 + x = -3.12757936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.12757936 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.12757936 + 0.5 x = -3.12757936 + 0.5 Combine like terms: -3.12757936 + 0.5 = -2.62757936 x = -2.62757936 Simplifying x = -2.62757936Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.62757936, -2.62757936}Solution
x = {3.62757936, -2.62757936}
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