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Simplifying 0 = -40x2 + 1360x + 16760 Reorder the terms: 0 = 16760 + 1360x + -40x2 Solving 0 = 16760 + 1360x + -40x2 Solving for variable 'x'. Combine like terms: 0 + -16760 = -16760 -16760 + -1360x + 40x2 = 16760 + 1360x + -40x2 + -16760 + -1360x + 40x2 Reorder the terms: -16760 + -1360x + 40x2 = 16760 + -16760 + 1360x + -1360x + -40x2 + 40x2 Combine like terms: 16760 + -16760 = 0 -16760 + -1360x + 40x2 = 0 + 1360x + -1360x + -40x2 + 40x2 -16760 + -1360x + 40x2 = 1360x + -1360x + -40x2 + 40x2 Combine like terms: 1360x + -1360x = 0 -16760 + -1360x + 40x2 = 0 + -40x2 + 40x2 -16760 + -1360x + 40x2 = -40x2 + 40x2 Combine like terms: -40x2 + 40x2 = 0 -16760 + -1360x + 40x2 = 0 Factor out the Greatest Common Factor (GCF), '40'. 40(-419 + -34x + x2) = 0 Ignore the factor 40.Subproblem 1
Set the factor '(-419 + -34x + x2)' equal to zero and attempt to solve: Simplifying -419 + -34x + x2 = 0 Solving -419 + -34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '419' to each side of the equation. -419 + -34x + 419 + x2 = 0 + 419 Reorder the terms: -419 + 419 + -34x + x2 = 0 + 419 Combine like terms: -419 + 419 = 0 0 + -34x + x2 = 0 + 419 -34x + x2 = 0 + 419 Combine like terms: 0 + 419 = 419 -34x + x2 = 419 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 419 + 289 Reorder the terms: 289 + -34x + x2 = 419 + 289 Combine like terms: 419 + 289 = 708 289 + -34x + x2 = 708 Factor a perfect square on the left side: (x + -17)(x + -17) = 708 Calculate the square root of the right side: 26.608269391 Break this problem into two subproblems by setting (x + -17) equal to 26.608269391 and -26.608269391.Subproblem 1
x + -17 = 26.608269391 Simplifying x + -17 = 26.608269391 Reorder the terms: -17 + x = 26.608269391 Solving -17 + x = 26.608269391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 26.608269391 + 17 Combine like terms: -17 + 17 = 0 0 + x = 26.608269391 + 17 x = 26.608269391 + 17 Combine like terms: 26.608269391 + 17 = 43.608269391 x = 43.608269391 Simplifying x = 43.608269391Subproblem 2
x + -17 = -26.608269391 Simplifying x + -17 = -26.608269391 Reorder the terms: -17 + x = -26.608269391 Solving -17 + x = -26.608269391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -26.608269391 + 17 Combine like terms: -17 + 17 = 0 0 + x = -26.608269391 + 17 x = -26.608269391 + 17 Combine like terms: -26.608269391 + 17 = -9.608269391 x = -9.608269391 Simplifying x = -9.608269391Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.608269391, -9.608269391}Solution
x = {43.608269391, -9.608269391}
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