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Simplifying 4x2 + 136x = 460 Reorder the terms: 136x + 4x2 = 460 Solving 136x + 4x2 = 460 Solving for variable 'x'. Reorder the terms: -460 + 136x + 4x2 = 460 + -460 Combine like terms: 460 + -460 = 0 -460 + 136x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-115 + 34x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-115 + 34x + x2)' equal to zero and attempt to solve: Simplifying -115 + 34x + x2 = 0 Solving -115 + 34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + 34x + 115 + x2 = 0 + 115 Reorder the terms: -115 + 115 + 34x + x2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + 34x + x2 = 0 + 115 34x + x2 = 0 + 115 Combine like terms: 0 + 115 = 115 34x + x2 = 115 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 = 115 + 289 Reorder the terms: 289 + 34x + x2 = 115 + 289 Combine like terms: 115 + 289 = 404 289 + 34x + x2 = 404 Factor a perfect square on the left side: (x + 17)(x + 17) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (x + 17) equal to 20.099751242 and -20.099751242.Subproblem 1
x + 17 = 20.099751242 Simplifying x + 17 = 20.099751242 Reorder the terms: 17 + x = 20.099751242 Solving 17 + x = 20.099751242 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 = 20.099751242 + -17 Combine like terms: 17 + -17 = 0 0 + x = 20.099751242 + -17 x = 20.099751242 + -17 Combine like terms: 20.099751242 + -17 = 3.099751242 x = 3.099751242 Simplifying x = 3.099751242Subproblem 2
x + 17 = -20.099751242 Simplifying x + 17 = -20.099751242 Reorder the terms: 17 + x = -20.099751242 Solving 17 + x = -20.099751242 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 = -20.099751242 + -17 Combine like terms: 17 + -17 = 0 0 + x = -20.099751242 + -17 x = -20.099751242 + -17 Combine like terms: -20.099751242 + -17 = -37.099751242 x = -37.099751242 Simplifying x = -37.099751242Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.099751242, -37.099751242}Solution
x = {3.099751242, -37.099751242}
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