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Simplifying 3x2 + 36x + 32 = 0 Reorder the terms: 32 + 36x + 3x2 = 0 Solving 32 + 36x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.66666667 + 12x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + 12x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + 12x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + 12x + x2 = 0 + -10.66666667 12x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 12x + x2 = -10.66666667 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 = -10.66666667 + 36 Reorder the terms: 36 + 12x + x2 = -10.66666667 + 36 Combine like terms: -10.66666667 + 36 = 25.33333333 36 + 12x + x2 = 25.33333333 Factor a perfect square on the left side: (x + 6)(x + 6) = 25.33333333 Calculate the square root of the right side: 5.033222957 Break this problem into two subproblems by setting (x + 6) equal to 5.033222957 and -5.033222957.Subproblem 1
x + 6 = 5.033222957 Simplifying x + 6 = 5.033222957 Reorder the terms: 6 + x = 5.033222957 Solving 6 + x = 5.033222957 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 = 5.033222957 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.033222957 + -6 x = 5.033222957 + -6 Combine like terms: 5.033222957 + -6 = -0.966777043 x = -0.966777043 Simplifying x = -0.966777043Subproblem 2
x + 6 = -5.033222957 Simplifying x + 6 = -5.033222957 Reorder the terms: 6 + x = -5.033222957 Solving 6 + x = -5.033222957 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 = -5.033222957 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.033222957 + -6 x = -5.033222957 + -6 Combine like terms: -5.033222957 + -6 = -11.033222957 x = -11.033222957 Simplifying x = -11.033222957Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.966777043, -11.033222957}
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