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Simplifying x2 + 26x + -380 = 0 Reorder the terms: -380 + 26x + x2 = 0 Solving -380 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '380' to each side of the equation. -380 + 26x + 380 + x2 = 0 + 380 Reorder the terms: -380 + 380 + 26x + x2 = 0 + 380 Combine like terms: -380 + 380 = 0 0 + 26x + x2 = 0 + 380 26x + x2 = 0 + 380 Combine like terms: 0 + 380 = 380 26x + x2 = 380 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 = 380 + 169 Reorder the terms: 169 + 26x + x2 = 380 + 169 Combine like terms: 380 + 169 = 549 169 + 26x + x2 = 549 Factor a perfect square on the left side: (x + 13)(x + 13) = 549 Calculate the square root of the right side: 23.430749028 Break this problem into two subproblems by setting (x + 13) equal to 23.430749028 and -23.430749028.Subproblem 1
x + 13 = 23.430749028 Simplifying x + 13 = 23.430749028 Reorder the terms: 13 + x = 23.430749028 Solving 13 + x = 23.430749028 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 = 23.430749028 + -13 Combine like terms: 13 + -13 = 0 0 + x = 23.430749028 + -13 x = 23.430749028 + -13 Combine like terms: 23.430749028 + -13 = 10.430749028 x = 10.430749028 Simplifying x = 10.430749028Subproblem 2
x + 13 = -23.430749028 Simplifying x + 13 = -23.430749028 Reorder the terms: 13 + x = -23.430749028 Solving 13 + x = -23.430749028 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 = -23.430749028 + -13 Combine like terms: 13 + -13 = 0 0 + x = -23.430749028 + -13 x = -23.430749028 + -13 Combine like terms: -23.430749028 + -13 = -36.430749028 x = -36.430749028 Simplifying x = -36.430749028Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.430749028, -36.430749028}
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