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Simplifying x2 + 26x + 138 = 0 Reorder the terms: 138 + 26x + x2 = 0 Solving 138 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-138' to each side of the equation. 138 + 26x + -138 + x2 = 0 + -138 Reorder the terms: 138 + -138 + 26x + x2 = 0 + -138 Combine like terms: 138 + -138 = 0 0 + 26x + x2 = 0 + -138 26x + x2 = 0 + -138 Combine like terms: 0 + -138 = -138 26x + x2 = -138 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 = -138 + 169 Reorder the terms: 169 + 26x + x2 = -138 + 169 Combine like terms: -138 + 169 = 31 169 + 26x + x2 = 31 Factor a perfect square on the left side: (x + 13)(x + 13) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 13) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 13 = 5.567764363 Simplifying x + 13 = 5.567764363 Reorder the terms: 13 + x = 5.567764363 Solving 13 + x = 5.567764363 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 = 5.567764363 + -13 Combine like terms: 13 + -13 = 0 0 + x = 5.567764363 + -13 x = 5.567764363 + -13 Combine like terms: 5.567764363 + -13 = -7.432235637 x = -7.432235637 Simplifying x = -7.432235637Subproblem 2
x + 13 = -5.567764363 Simplifying x + 13 = -5.567764363 Reorder the terms: 13 + x = -5.567764363 Solving 13 + x = -5.567764363 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 = -5.567764363 + -13 Combine like terms: 13 + -13 = 0 0 + x = -5.567764363 + -13 x = -5.567764363 + -13 Combine like terms: -5.567764363 + -13 = -18.567764363 x = -18.567764363 Simplifying x = -18.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.432235637, -18.567764363}
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