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Simplifying x2 + 26x + 60 = 0 Reorder the terms: 60 + 26x + x2 = 0 Solving 60 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 26x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 26x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 26x + x2 = 0 + -60 26x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 26x + x2 = -60 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -60 + 169 Reorder the terms: 169 + 26x + x2 = -60 + 169 Combine like terms: -60 + 169 = 109 169 + 26x + x2 = 109 Factor a perfect square on the left side: (x + 13)(x + 13) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 13) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 13 = 10.440306509 Simplifying x + 13 = 10.440306509 Reorder the terms: 13 + x = 10.440306509 Solving 13 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 10.440306509 + -13 Combine like terms: 13 + -13 = 0 0 + x = 10.440306509 + -13 x = 10.440306509 + -13 Combine like terms: 10.440306509 + -13 = -2.559693491 x = -2.559693491 Simplifying x = -2.559693491Subproblem 2
x + 13 = -10.440306509 Simplifying x + 13 = -10.440306509 Reorder the terms: 13 + x = -10.440306509 Solving 13 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -10.440306509 + -13 Combine like terms: 13 + -13 = 0 0 + x = -10.440306509 + -13 x = -10.440306509 + -13 Combine like terms: -10.440306509 + -13 = -23.440306509 x = -23.440306509 Simplifying x = -23.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.559693491, -23.440306509}
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