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Simplifying x2 + 12x + 1 = -2 Reorder the terms: 1 + 12x + x2 = -2 Solving 1 + 12x + x2 = -2 Solving for variable 'x'. Reorder the terms: 1 + 2 + 12x + x2 = -2 + 2 Combine like terms: 1 + 2 = 3 3 + 12x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 3 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 12x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 12x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 12x + x2 = 0 + -3 12x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 12x + x2 = -3 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 = -3 + 36 Reorder the terms: 36 + 12x + x2 = -3 + 36 Combine like terms: -3 + 36 = 33 36 + 12x + x2 = 33 Factor a perfect square on the left side: (x + 6)(x + 6) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 6) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 6 = 5.744562647 Simplifying x + 6 = 5.744562647 Reorder the terms: 6 + x = 5.744562647 Solving 6 + x = 5.744562647 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 = 5.744562647 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.744562647 + -6 x = 5.744562647 + -6 Combine like terms: 5.744562647 + -6 = -0.255437353 x = -0.255437353 Simplifying x = -0.255437353Subproblem 2
x + 6 = -5.744562647 Simplifying x + 6 = -5.744562647 Reorder the terms: 6 + x = -5.744562647 Solving 6 + x = -5.744562647 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 = -5.744562647 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.744562647 + -6 x = -5.744562647 + -6 Combine like terms: -5.744562647 + -6 = -11.744562647 x = -11.744562647 Simplifying x = -11.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.255437353, -11.744562647}
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