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Simplifying 6x2 + -36x + -49 = 0 Reorder the terms: -49 + -36x + 6x2 = 0 Solving -49 + -36x + 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'. -8.166666667 + -6x + x2 = 0 Move the constant term to the right: Add '8.166666667' to each side of the equation. -8.166666667 + -6x + 8.166666667 + x2 = 0 + 8.166666667 Reorder the terms: -8.166666667 + 8.166666667 + -6x + x2 = 0 + 8.166666667 Combine like terms: -8.166666667 + 8.166666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + 8.166666667 -6x + x2 = 0 + 8.166666667 Combine like terms: 0 + 8.166666667 = 8.166666667 -6x + x2 = 8.166666667 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 = 8.166666667 + 9 Reorder the terms: 9 + -6x + x2 = 8.166666667 + 9 Combine like terms: 8.166666667 + 9 = 17.166666667 9 + -6x + x2 = 17.166666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 17.166666667 Calculate the square root of the right side: 4.143267632 Break this problem into two subproblems by setting (x + -3) equal to 4.143267632 and -4.143267632.Subproblem 1
x + -3 = 4.143267632 Simplifying x + -3 = 4.143267632 Reorder the terms: -3 + x = 4.143267632 Solving -3 + x = 4.143267632 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 = 4.143267632 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.143267632 + 3 x = 4.143267632 + 3 Combine like terms: 4.143267632 + 3 = 7.143267632 x = 7.143267632 Simplifying x = 7.143267632Subproblem 2
x + -3 = -4.143267632 Simplifying x + -3 = -4.143267632 Reorder the terms: -3 + x = -4.143267632 Solving -3 + x = -4.143267632 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 = -4.143267632 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.143267632 + 3 x = -4.143267632 + 3 Combine like terms: -4.143267632 + 3 = -1.143267632 x = -1.143267632 Simplifying x = -1.143267632Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.143267632, -1.143267632}
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