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Simplifying x2 + -2x2 = 400x + 9999 Combine like terms: x2 + -2x2 = -1x2 -1x2 = 400x + 9999 Reorder the terms: -1x2 = 9999 + 400x Solving -1x2 = 9999 + 400x Solving for variable 'x'. Reorder the terms: -9999 + -400x + -1x2 = 9999 + 400x + -9999 + -400x Reorder the terms: -9999 + -400x + -1x2 = 9999 + -9999 + 400x + -400x Combine like terms: 9999 + -9999 = 0 -9999 + -400x + -1x2 = 0 + 400x + -400x -9999 + -400x + -1x2 = 400x + -400x Combine like terms: 400x + -400x = 0 -9999 + -400x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9999 + 400x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9999 + 400x + x2)' equal to zero and attempt to solve: Simplifying 9999 + 400x + x2 = 0 Solving 9999 + 400x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9999' to each side of the equation. 9999 + 400x + -9999 + x2 = 0 + -9999 Reorder the terms: 9999 + -9999 + 400x + x2 = 0 + -9999 Combine like terms: 9999 + -9999 = 0 0 + 400x + x2 = 0 + -9999 400x + x2 = 0 + -9999 Combine like terms: 0 + -9999 = -9999 400x + x2 = -9999 The x term is 400x. Take half its coefficient (200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. 400x + 40000 + x2 = -9999 + 40000 Reorder the terms: 40000 + 400x + x2 = -9999 + 40000 Combine like terms: -9999 + 40000 = 30001 40000 + 400x + x2 = 30001 Factor a perfect square on the left side: (x + 200)(x + 200) = 30001 Calculate the square root of the right side: 173.207967484 Break this problem into two subproblems by setting (x + 200) equal to 173.207967484 and -173.207967484.Subproblem 1
x + 200 = 173.207967484 Simplifying x + 200 = 173.207967484 Reorder the terms: 200 + x = 173.207967484 Solving 200 + x = 173.207967484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = 173.207967484 + -200 Combine like terms: 200 + -200 = 0 0 + x = 173.207967484 + -200 x = 173.207967484 + -200 Combine like terms: 173.207967484 + -200 = -26.792032516 x = -26.792032516 Simplifying x = -26.792032516Subproblem 2
x + 200 = -173.207967484 Simplifying x + 200 = -173.207967484 Reorder the terms: 200 + x = -173.207967484 Solving 200 + x = -173.207967484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = -173.207967484 + -200 Combine like terms: 200 + -200 = 0 0 + x = -173.207967484 + -200 x = -173.207967484 + -200 Combine like terms: -173.207967484 + -200 = -373.207967484 x = -373.207967484 Simplifying x = -373.207967484Solution
The solution to the problem is based on the solutions from the subproblems. x = {-26.792032516, -373.207967484}Solution
x = {-26.792032516, -373.207967484}
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