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Simplifying 3x2 + 36x + 31 = 0 Reorder the terms: 31 + 36x + 3x2 = 0 Solving 31 + 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'. 10.33333333 + 12x + x2 = 0 Move the constant term to the right: Add '-10.33333333' to each side of the equation. 10.33333333 + 12x + -10.33333333 + x2 = 0 + -10.33333333 Reorder the terms: 10.33333333 + -10.33333333 + 12x + x2 = 0 + -10.33333333 Combine like terms: 10.33333333 + -10.33333333 = 0.00000000 0.00000000 + 12x + x2 = 0 + -10.33333333 12x + x2 = 0 + -10.33333333 Combine like terms: 0 + -10.33333333 = -10.33333333 12x + x2 = -10.33333333 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 = -10.33333333 + 36 Reorder the terms: 36 + 12x + x2 = -10.33333333 + 36 Combine like terms: -10.33333333 + 36 = 25.66666667 36 + 12x + x2 = 25.66666667 Factor a perfect square on the left side: (x + 6)(x + 6) = 25.66666667 Calculate the square root of the right side: 5.066228052 Break this problem into two subproblems by setting (x + 6) equal to 5.066228052 and -5.066228052.Subproblem 1
x + 6 = 5.066228052 Simplifying x + 6 = 5.066228052 Reorder the terms: 6 + x = 5.066228052 Solving 6 + x = 5.066228052 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 = 5.066228052 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.066228052 + -6 x = 5.066228052 + -6 Combine like terms: 5.066228052 + -6 = -0.933771948 x = -0.933771948 Simplifying x = -0.933771948Subproblem 2
x + 6 = -5.066228052 Simplifying x + 6 = -5.066228052 Reorder the terms: 6 + x = -5.066228052 Solving 6 + x = -5.066228052 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 = -5.066228052 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.066228052 + -6 x = -5.066228052 + -6 Combine like terms: -5.066228052 + -6 = -11.066228052 x = -11.066228052 Simplifying x = -11.066228052Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.933771948, -11.066228052}
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