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Simplifying x2 + 13x + -138 = 0 Reorder the terms: -138 + 13x + x2 = 0 Solving -138 + 13x + 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 + 13x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + 13x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + 13x + x2 = 0 + 138 13x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 13x + x2 = 138 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 138 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 138 + 42.25 Combine like terms: 138 + 42.25 = 180.25 42.25 + 13x + x2 = 180.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + 6.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + 6.5 = 13.425721582 Simplifying x + 6.5 = 13.425721582 Reorder the terms: 6.5 + x = 13.425721582 Solving 6.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 13.425721582 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 13.425721582 + -6.5 x = 13.425721582 + -6.5 Combine like terms: 13.425721582 + -6.5 = 6.925721582 x = 6.925721582 Simplifying x = 6.925721582Subproblem 2
x + 6.5 = -13.425721582 Simplifying x + 6.5 = -13.425721582 Reorder the terms: 6.5 + x = -13.425721582 Solving 6.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -13.425721582 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -13.425721582 + -6.5 x = -13.425721582 + -6.5 Combine like terms: -13.425721582 + -6.5 = -19.925721582 x = -19.925721582 Simplifying x = -19.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.925721582, -19.925721582}
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