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Simplifying 36x2 + -21x + -1 = 0 Reorder the terms: -1 + -21x + 36x2 = 0 Solving -1 + -21x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.02777777778 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + -0.5833333333x + 0.02777777778 + x2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + -0.5833333333x + x2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + -0.5833333333x + x2 = 0 + 0.02777777778 -0.5833333333x + x2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 -0.5833333333x + x2 = 0.02777777778 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 0.02777777778 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 0.02777777778 + 0.08506944446 Combine like terms: 0.02777777778 + 0.08506944446 = 0.11284722224 0.08506944446 + -0.5833333333x + x2 = 0.11284722224 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.11284722224 Calculate the square root of the right side: 0.335927406 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.335927406 and -0.335927406.Subproblem 1
x + -0.2916666667 = 0.335927406 Simplifying x + -0.2916666667 = 0.335927406 Reorder the terms: -0.2916666667 + x = 0.335927406 Solving -0.2916666667 + x = 0.335927406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.335927406 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.335927406 + 0.2916666667 x = 0.335927406 + 0.2916666667 Combine like terms: 0.335927406 + 0.2916666667 = 0.6275940727 x = 0.6275940727 Simplifying x = 0.6275940727Subproblem 2
x + -0.2916666667 = -0.335927406 Simplifying x + -0.2916666667 = -0.335927406 Reorder the terms: -0.2916666667 + x = -0.335927406 Solving -0.2916666667 + x = -0.335927406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.335927406 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.335927406 + 0.2916666667 x = -0.335927406 + 0.2916666667 Combine like terms: -0.335927406 + 0.2916666667 = -0.0442607393 x = -0.0442607393 Simplifying x = -0.0442607393Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6275940727, -0.0442607393}
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