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Simplifying 12x2 + -14x + -35 = 0 Reorder the terms: -35 + -14x + 12x2 = 0 Solving -35 + -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'. -2.916666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '2.916666667' to each side of the equation. -2.916666667 + -1.166666667x + 2.916666667 + x2 = 0 + 2.916666667 Reorder the terms: -2.916666667 + 2.916666667 + -1.166666667x + x2 = 0 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 2.916666667 -1.166666667x + x2 = 0 + 2.916666667 Combine like terms: 0 + 2.916666667 = 2.916666667 -1.166666667x + x2 = 2.916666667 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 = 2.916666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 2.916666667 + 0.3402777780 Combine like terms: 2.916666667 + 0.3402777780 = 3.256944445 0.3402777780 + -1.166666667x + x2 = 3.256944445 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 3.256944445 Calculate the square root of the right side: 1.804700652 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.804700652 and -1.804700652.Subproblem 1
x + -0.5833333335 = 1.804700652 Simplifying x + -0.5833333335 = 1.804700652 Reorder the terms: -0.5833333335 + x = 1.804700652 Solving -0.5833333335 + x = 1.804700652 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 = 1.804700652 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.804700652 + 0.5833333335 x = 1.804700652 + 0.5833333335 Combine like terms: 1.804700652 + 0.5833333335 = 2.3880339855 x = 2.3880339855 Simplifying x = 2.3880339855Subproblem 2
x + -0.5833333335 = -1.804700652 Simplifying x + -0.5833333335 = -1.804700652 Reorder the terms: -0.5833333335 + x = -1.804700652 Solving -0.5833333335 + x = -1.804700652 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 = -1.804700652 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.804700652 + 0.5833333335 x = -1.804700652 + 0.5833333335 Combine like terms: -1.804700652 + 0.5833333335 = -1.2213673185 x = -1.2213673185 Simplifying x = -1.2213673185Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3880339855, -1.2213673185}
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