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Simplifying x2 + 12x + 11 = 5 Reorder the terms: 11 + 12x + x2 = 5 Solving 11 + 12x + x2 = 5 Solving for variable 'x'. Reorder the terms: 11 + -5 + 12x + x2 = 5 + -5 Combine like terms: 11 + -5 = 6 6 + 12x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 6 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 12x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 12x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 12x + x2 = 0 + -6 12x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 12x + x2 = -6 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 = -6 + 36 Reorder the terms: 36 + 12x + x2 = -6 + 36 Combine like terms: -6 + 36 = 30 36 + 12x + x2 = 30 Factor a perfect square on the left side: (x + 6)(x + 6) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 6) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 6 = 5.477225575 Simplifying x + 6 = 5.477225575 Reorder the terms: 6 + x = 5.477225575 Solving 6 + x = 5.477225575 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 = 5.477225575 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.477225575 + -6 x = 5.477225575 + -6 Combine like terms: 5.477225575 + -6 = -0.522774425 x = -0.522774425 Simplifying x = -0.522774425Subproblem 2
x + 6 = -5.477225575 Simplifying x + 6 = -5.477225575 Reorder the terms: 6 + x = -5.477225575 Solving 6 + x = -5.477225575 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 = -5.477225575 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.477225575 + -6 x = -5.477225575 + -6 Combine like terms: -5.477225575 + -6 = -11.477225575 x = -11.477225575 Simplifying x = -11.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.522774425, -11.477225575}
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