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Simplifying x2 + 12x + 5 = 3 Reorder the terms: 5 + 12x + x2 = 3 Solving 5 + 12x + x2 = 3 Solving for variable 'x'. Reorder the terms: 5 + -3 + 12x + x2 = 3 + -3 Combine like terms: 5 + -3 = 2 2 + 12x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 2 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 12x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 12x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 12x + x2 = 0 + -2 12x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 12x + x2 = -2 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 = -2 + 36 Reorder the terms: 36 + 12x + x2 = -2 + 36 Combine like terms: -2 + 36 = 34 36 + 12x + x2 = 34 Factor a perfect square on the left side: (x + 6)(x + 6) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 6) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 6 = 5.830951895 Simplifying x + 6 = 5.830951895 Reorder the terms: 6 + x = 5.830951895 Solving 6 + x = 5.830951895 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 = 5.830951895 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.830951895 + -6 x = 5.830951895 + -6 Combine like terms: 5.830951895 + -6 = -0.169048105 x = -0.169048105 Simplifying x = -0.169048105Subproblem 2
x + 6 = -5.830951895 Simplifying x + 6 = -5.830951895 Reorder the terms: 6 + x = -5.830951895 Solving 6 + x = -5.830951895 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 = -5.830951895 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.830951895 + -6 x = -5.830951895 + -6 Combine like terms: -5.830951895 + -6 = -11.830951895 x = -11.830951895 Simplifying x = -11.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.169048105, -11.830951895}
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