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Simplifying 6x2 + 36x = -41 Reorder the terms: 36x + 6x2 = -41 Solving 36x + 6x2 = -41 Solving for variable 'x'. Reorder the terms: 41 + 36x + 6x2 = -41 + 41 Combine like terms: -41 + 41 = 0 41 + 36x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 6.833333333 + 6x + x2 = 0 Move the constant term to the right: Add '-6.833333333' to each side of the equation. 6.833333333 + 6x + -6.833333333 + x2 = 0 + -6.833333333 Reorder the terms: 6.833333333 + -6.833333333 + 6x + x2 = 0 + -6.833333333 Combine like terms: 6.833333333 + -6.833333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + -6.833333333 6x + x2 = 0 + -6.833333333 Combine like terms: 0 + -6.833333333 = -6.833333333 6x + x2 = -6.833333333 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -6.833333333 + 9 Reorder the terms: 9 + 6x + x2 = -6.833333333 + 9 Combine like terms: -6.833333333 + 9 = 2.166666667 9 + 6x + x2 = 2.166666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 2.166666667 Calculate the square root of the right side: 1.471960145 Break this problem into two subproblems by setting (x + 3) equal to 1.471960145 and -1.471960145.Subproblem 1
x + 3 = 1.471960145 Simplifying x + 3 = 1.471960145 Reorder the terms: 3 + x = 1.471960145 Solving 3 + x = 1.471960145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.471960145 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.471960145 + -3 x = 1.471960145 + -3 Combine like terms: 1.471960145 + -3 = -1.528039855 x = -1.528039855 Simplifying x = -1.528039855Subproblem 2
x + 3 = -1.471960145 Simplifying x + 3 = -1.471960145 Reorder the terms: 3 + x = -1.471960145 Solving 3 + x = -1.471960145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.471960145 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.471960145 + -3 x = -1.471960145 + -3 Combine like terms: -1.471960145 + -3 = -4.471960145 x = -4.471960145 Simplifying x = -4.471960145Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.528039855, -4.471960145}
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