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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 = 18.567764363 x = 18.567764363 Simplifying x = 18.567764363Subproblem 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 = 7.432235637 x = 7.432235637 Simplifying x = 7.432235637Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.567764363, 7.432235637}
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