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Simplifying 460 = (2x + 42)(2x + 26) Reorder the terms: 460 = (42 + 2x)(2x + 26) Reorder the terms: 460 = (42 + 2x)(26 + 2x) Multiply (42 + 2x) * (26 + 2x) 460 = (42(26 + 2x) + 2x * (26 + 2x)) 460 = ((26 * 42 + 2x * 42) + 2x * (26 + 2x)) 460 = ((1092 + 84x) + 2x * (26 + 2x)) 460 = (1092 + 84x + (26 * 2x + 2x * 2x)) 460 = (1092 + 84x + (52x + 4x2)) Combine like terms: 84x + 52x = 136x 460 = (1092 + 136x + 4x2) Solving 460 = 1092 + 136x + 4x2 Solving for variable 'x'. Combine like terms: 460 + -1092 = -632 -632 + -136x + -4x2 = 1092 + 136x + 4x2 + -1092 + -136x + -4x2 Reorder the terms: -632 + -136x + -4x2 = 1092 + -1092 + 136x + -136x + 4x2 + -4x2 Combine like terms: 1092 + -1092 = 0 -632 + -136x + -4x2 = 0 + 136x + -136x + 4x2 + -4x2 -632 + -136x + -4x2 = 136x + -136x + 4x2 + -4x2 Combine like terms: 136x + -136x = 0 -632 + -136x + -4x2 = 0 + 4x2 + -4x2 -632 + -136x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -632 + -136x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(158 + 34x + x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(158 + 34x + x2)' equal to zero and attempt to solve: Simplifying 158 + 34x + x2 = 0 Solving 158 + 34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-158' to each side of the equation. 158 + 34x + -158 + x2 = 0 + -158 Reorder the terms: 158 + -158 + 34x + x2 = 0 + -158 Combine like terms: 158 + -158 = 0 0 + 34x + x2 = 0 + -158 34x + x2 = 0 + -158 Combine like terms: 0 + -158 = -158 34x + x2 = -158 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 = -158 + 289 Reorder the terms: 289 + 34x + x2 = -158 + 289 Combine like terms: -158 + 289 = 131 289 + 34x + x2 = 131 Factor a perfect square on the left side: (x + 17)(x + 17) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x + 17) equal to 11.445523142 and -11.445523142.Subproblem 1
x + 17 = 11.445523142 Simplifying x + 17 = 11.445523142 Reorder the terms: 17 + x = 11.445523142 Solving 17 + x = 11.445523142 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 = 11.445523142 + -17 Combine like terms: 17 + -17 = 0 0 + x = 11.445523142 + -17 x = 11.445523142 + -17 Combine like terms: 11.445523142 + -17 = -5.554476858 x = -5.554476858 Simplifying x = -5.554476858Subproblem 2
x + 17 = -11.445523142 Simplifying x + 17 = -11.445523142 Reorder the terms: 17 + x = -11.445523142 Solving 17 + x = -11.445523142 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 = -11.445523142 + -17 Combine like terms: 17 + -17 = 0 0 + x = -11.445523142 + -17 x = -11.445523142 + -17 Combine like terms: -11.445523142 + -17 = -28.445523142 x = -28.445523142 Simplifying x = -28.445523142Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.554476858, -28.445523142}Solution
x = {-5.554476858, -28.445523142}
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