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Simplifying 2x2 + 34x = 7208 Reorder the terms: 34x + 2x2 = 7208 Solving 34x + 2x2 = 7208 Solving for variable 'x'. Reorder the terms: -7208 + 34x + 2x2 = 7208 + -7208 Combine like terms: 7208 + -7208 = 0 -7208 + 34x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3604 + 17x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3604 + 17x + x2)' equal to zero and attempt to solve: Simplifying -3604 + 17x + x2 = 0 Solving -3604 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3604' to each side of the equation. -3604 + 17x + 3604 + x2 = 0 + 3604 Reorder the terms: -3604 + 3604 + 17x + x2 = 0 + 3604 Combine like terms: -3604 + 3604 = 0 0 + 17x + x2 = 0 + 3604 17x + x2 = 0 + 3604 Combine like terms: 0 + 3604 = 3604 17x + x2 = 3604 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 3604 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 3604 + 72.25 Combine like terms: 3604 + 72.25 = 3676.25 72.25 + 17x + x2 = 3676.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 3676.25 Calculate the square root of the right side: 60.632087215 Break this problem into two subproblems by setting (x + 8.5) equal to 60.632087215 and -60.632087215.Subproblem 1
x + 8.5 = 60.632087215 Simplifying x + 8.5 = 60.632087215 Reorder the terms: 8.5 + x = 60.632087215 Solving 8.5 + x = 60.632087215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 60.632087215 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 60.632087215 + -8.5 x = 60.632087215 + -8.5 Combine like terms: 60.632087215 + -8.5 = 52.132087215 x = 52.132087215 Simplifying x = 52.132087215Subproblem 2
x + 8.5 = -60.632087215 Simplifying x + 8.5 = -60.632087215 Reorder the terms: 8.5 + x = -60.632087215 Solving 8.5 + x = -60.632087215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -60.632087215 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -60.632087215 + -8.5 x = -60.632087215 + -8.5 Combine like terms: -60.632087215 + -8.5 = -69.132087215 x = -69.132087215 Simplifying x = -69.132087215Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.132087215, -69.132087215}Solution
x = {52.132087215, -69.132087215}
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