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Simplifying x2 + 12x + -164 = 0 Reorder the terms: -164 + 12x + x2 = 0 Solving -164 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + 12x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + 12x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + 12x + x2 = 0 + 164 12x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 12x + x2 = 164 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 = 164 + 36 Reorder the terms: 36 + 12x + x2 = 164 + 36 Combine like terms: 164 + 36 = 200 36 + 12x + x2 = 200 Factor a perfect square on the left side: (x + 6)(x + 6) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 6) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 6 = 14.142135624 Simplifying x + 6 = 14.142135624 Reorder the terms: 6 + x = 14.142135624 Solving 6 + x = 14.142135624 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 = 14.142135624 + -6 Combine like terms: 6 + -6 = 0 0 + x = 14.142135624 + -6 x = 14.142135624 + -6 Combine like terms: 14.142135624 + -6 = 8.142135624 x = 8.142135624 Simplifying x = 8.142135624Subproblem 2
x + 6 = -14.142135624 Simplifying x + 6 = -14.142135624 Reorder the terms: 6 + x = -14.142135624 Solving 6 + x = -14.142135624 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 = -14.142135624 + -6 Combine like terms: 6 + -6 = 0 0 + x = -14.142135624 + -6 x = -14.142135624 + -6 Combine like terms: -14.142135624 + -6 = -20.142135624 x = -20.142135624 Simplifying x = -20.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.142135624, -20.142135624}
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