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Simplifying (12x2) + -14x + -55 = 0 Reorder the terms: -55 + -14x + (12x2) = 0 Solving -55 + -14x + (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 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '4.583333333' to each side of the equation. -4.583333333 + -1.166666667x + 4.583333333 + x2 = 0 + 4.583333333 Reorder the terms: -4.583333333 + 4.583333333 + -1.166666667x + x2 = 0 + 4.583333333 Combine like terms: -4.583333333 + 4.583333333 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 4.583333333 -1.166666667x + x2 = 0 + 4.583333333 Combine like terms: 0 + 4.583333333 = 4.583333333 -1.166666667x + x2 = 4.583333333 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 4.583333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 4.583333333 + 0.3402777780 Combine like terms: 4.583333333 + 0.3402777780 = 4.923611111 0.3402777780 + -1.166666667x + x2 = 4.923611111 Factor a perfect square on the left side: ((x) + -0.5833333335)((x) + -0.5833333335) = 4.923611111 Calculate the square root of the right side: 2.218921159 Break this problem into two subproblems by setting ((x) + -0.5833333335) equal to 2.218921159 and -2.218921159.Subproblem 1
(x) + -0.5833333335 = 2.218921159 Simplifying (x) + -0.5833333335 = 2.218921159 x + -0.5833333335 = 2.218921159 Reorder the terms: -0.5833333335 + x = 2.218921159 Solving -0.5833333335 + x = 2.218921159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 2.218921159 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 2.218921159 + 0.5833333335 x = 2.218921159 + 0.5833333335 Combine like terms: 2.218921159 + 0.5833333335 = 2.8022544925 x = 2.8022544925 Simplifying x = 2.8022544925Subproblem 2
(x) + -0.5833333335 = -2.218921159 Simplifying (x) + -0.5833333335 = -2.218921159 x + -0.5833333335 = -2.218921159 Reorder the terms: -0.5833333335 + x = -2.218921159 Solving -0.5833333335 + x = -2.218921159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -2.218921159 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -2.218921159 + 0.5833333335 x = -2.218921159 + 0.5833333335 Combine like terms: -2.218921159 + 0.5833333335 = -1.6355878255 x = -1.6355878255 Simplifying x = -1.6355878255Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8022544925, -1.6355878255}
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