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Simplifying x2 + 12x + -169 = 0 Reorder the terms: -169 + 12x + x2 = 0 Solving -169 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '169' to each side of the equation. -169 + 12x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + 12x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 12x + x2 = 0 + 169 12x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 12x + x2 = 169 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 169 + 36 Reorder the terms: 36 + 12x + x2 = 169 + 36 Combine like terms: 169 + 36 = 205 36 + 12x + x2 = 205 Factor a perfect square on the left side: (x + 6)(x + 6) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + 6) equal to 14.317821063 and -14.317821063.Subproblem 1
x + 6 = 14.317821063 Simplifying x + 6 = 14.317821063 Reorder the terms: 6 + x = 14.317821063 Solving 6 + x = 14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 14.317821063 + -6 Combine like terms: 6 + -6 = 0 0 + x = 14.317821063 + -6 x = 14.317821063 + -6 Combine like terms: 14.317821063 + -6 = 8.317821063 x = 8.317821063 Simplifying x = 8.317821063Subproblem 2
x + 6 = -14.317821063 Simplifying x + 6 = -14.317821063 Reorder the terms: 6 + x = -14.317821063 Solving 6 + x = -14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -14.317821063 + -6 Combine like terms: 6 + -6 = 0 0 + x = -14.317821063 + -6 x = -14.317821063 + -6 Combine like terms: -14.317821063 + -6 = -20.317821063 x = -20.317821063 Simplifying x = -20.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.317821063, -20.317821063}
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