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Simplifying (12x2) + -7x + -55 = 0 Reorder the terms: -55 + -7x + (12x2) = 0 Solving -55 + -7x + (12x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4.583333333 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '4.583333333' to each side of the equation. -4.583333333 + -0.5833333333x + 4.583333333 + x2 = 0 + 4.583333333 Reorder the terms: -4.583333333 + 4.583333333 + -0.5833333333x + x2 = 0 + 4.583333333 Combine like terms: -4.583333333 + 4.583333333 = 0.000000000 0.000000000 + -0.5833333333x + x2 = 0 + 4.583333333 -0.5833333333x + x2 = 0 + 4.583333333 Combine like terms: 0 + 4.583333333 = 4.583333333 -0.5833333333x + x2 = 4.583333333 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 = 4.583333333 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 4.583333333 + 0.08506944446 Combine like terms: 4.583333333 + 0.08506944446 = 4.66840277746 0.08506944446 + -0.5833333333x + x2 = 4.66840277746 Factor a perfect square on the left side: ((x) + -0.2916666667)((x) + -0.2916666667) = 4.66840277746 Calculate the square root of the right side: 2.160648694 Break this problem into two subproblems by setting ((x) + -0.2916666667) equal to 2.160648694 and -2.160648694.Subproblem 1
(x) + -0.2916666667 = 2.160648694 Simplifying (x) + -0.2916666667 = 2.160648694 x + -0.2916666667 = 2.160648694 Reorder the terms: -0.2916666667 + x = 2.160648694 Solving -0.2916666667 + x = 2.160648694 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 = 2.160648694 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 2.160648694 + 0.2916666667 x = 2.160648694 + 0.2916666667 Combine like terms: 2.160648694 + 0.2916666667 = 2.4523153607 x = 2.4523153607 Simplifying x = 2.4523153607Subproblem 2
(x) + -0.2916666667 = -2.160648694 Simplifying (x) + -0.2916666667 = -2.160648694 x + -0.2916666667 = -2.160648694 Reorder the terms: -0.2916666667 + x = -2.160648694 Solving -0.2916666667 + x = -2.160648694 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 = -2.160648694 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -2.160648694 + 0.2916666667 x = -2.160648694 + 0.2916666667 Combine like terms: -2.160648694 + 0.2916666667 = -1.8689820273 x = -1.8689820273 Simplifying x = -1.8689820273Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4523153607, -1.8689820273}
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