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Simplifying 6x2 + 37x + -6 = 0 Reorder the terms: -6 + 37x + 6x2 = 0 Solving -6 + 37x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + 6.166666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 6.166666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 6.166666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6.166666667x + x2 = 0 + 1 6.166666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 6.166666667x + x2 = 1 The x term is 6.166666667x. Take half its coefficient (3.083333334). Square it (9.506944449) and add it to both sides. Add '9.506944449' to each side of the equation. 6.166666667x + 9.506944449 + x2 = 1 + 9.506944449 Reorder the terms: 9.506944449 + 6.166666667x + x2 = 1 + 9.506944449 Combine like terms: 1 + 9.506944449 = 10.506944449 9.506944449 + 6.166666667x + x2 = 10.506944449 Factor a perfect square on the left side: (x + 3.083333334)(x + 3.083333334) = 10.506944449 Calculate the square root of the right side: 3.241441724 Break this problem into two subproblems by setting (x + 3.083333334) equal to 3.241441724 and -3.241441724.Subproblem 1
x + 3.083333334 = 3.241441724 Simplifying x + 3.083333334 = 3.241441724 Reorder the terms: 3.083333334 + x = 3.241441724 Solving 3.083333334 + x = 3.241441724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.083333334' to each side of the equation. 3.083333334 + -3.083333334 + x = 3.241441724 + -3.083333334 Combine like terms: 3.083333334 + -3.083333334 = 0.000000000 0.000000000 + x = 3.241441724 + -3.083333334 x = 3.241441724 + -3.083333334 Combine like terms: 3.241441724 + -3.083333334 = 0.15810839 x = 0.15810839 Simplifying x = 0.15810839Subproblem 2
x + 3.083333334 = -3.241441724 Simplifying x + 3.083333334 = -3.241441724 Reorder the terms: 3.083333334 + x = -3.241441724 Solving 3.083333334 + x = -3.241441724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.083333334' to each side of the equation. 3.083333334 + -3.083333334 + x = -3.241441724 + -3.083333334 Combine like terms: 3.083333334 + -3.083333334 = 0.000000000 0.000000000 + x = -3.241441724 + -3.083333334 x = -3.241441724 + -3.083333334 Combine like terms: -3.241441724 + -3.083333334 = -6.324775058 x = -6.324775058 Simplifying x = -6.324775058Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.15810839, -6.324775058}
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