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Simplifying x2 + 12x + 6 = 936 Reorder the terms: 6 + 12x + x2 = 936 Solving 6 + 12x + x2 = 936 Solving for variable 'x'. Reorder the terms: 6 + -936 + 12x + x2 = 936 + -936 Combine like terms: 6 + -936 = -930 -930 + 12x + x2 = 936 + -936 Combine like terms: 936 + -936 = 0 -930 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '930' to each side of the equation. -930 + 12x + 930 + x2 = 0 + 930 Reorder the terms: -930 + 930 + 12x + x2 = 0 + 930 Combine like terms: -930 + 930 = 0 0 + 12x + x2 = 0 + 930 12x + x2 = 0 + 930 Combine like terms: 0 + 930 = 930 12x + x2 = 930 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 = 930 + 36 Reorder the terms: 36 + 12x + x2 = 930 + 36 Combine like terms: 930 + 36 = 966 36 + 12x + x2 = 966 Factor a perfect square on the left side: (x + 6)(x + 6) = 966 Calculate the square root of the right side: 31.080540536 Break this problem into two subproblems by setting (x + 6) equal to 31.080540536 and -31.080540536.Subproblem 1
x + 6 = 31.080540536 Simplifying x + 6 = 31.080540536 Reorder the terms: 6 + x = 31.080540536 Solving 6 + x = 31.080540536 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 = 31.080540536 + -6 Combine like terms: 6 + -6 = 0 0 + x = 31.080540536 + -6 x = 31.080540536 + -6 Combine like terms: 31.080540536 + -6 = 25.080540536 x = 25.080540536 Simplifying x = 25.080540536Subproblem 2
x + 6 = -31.080540536 Simplifying x + 6 = -31.080540536 Reorder the terms: 6 + x = -31.080540536 Solving 6 + x = -31.080540536 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 = -31.080540536 + -6 Combine like terms: 6 + -6 = 0 0 + x = -31.080540536 + -6 x = -31.080540536 + -6 Combine like terms: -31.080540536 + -6 = -37.080540536 x = -37.080540536 Simplifying x = -37.080540536Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.080540536, -37.080540536}
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