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Simplifying 12x2 + -14x + -7 = 0 Reorder the terms: -7 + -14x + 12x2 = 0 Solving -7 + -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'. -0.5833333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -1.166666667x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -1.166666667x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + 0.5833333333 -1.166666667x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -1.166666667x + x2 = 0.5833333333 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 = 0.5833333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.5833333333 + 0.3402777780 Combine like terms: 0.5833333333 + 0.3402777780 = 0.9236111113 0.3402777780 + -1.166666667x + x2 = 0.9236111113 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.9236111113 Calculate the square root of the right side: 0.961046883 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.961046883 and -0.961046883.Subproblem 1
x + -0.5833333335 = 0.961046883 Simplifying x + -0.5833333335 = 0.961046883 Reorder the terms: -0.5833333335 + x = 0.961046883 Solving -0.5833333335 + x = 0.961046883 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 = 0.961046883 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.961046883 + 0.5833333335 x = 0.961046883 + 0.5833333335 Combine like terms: 0.961046883 + 0.5833333335 = 1.5443802165 x = 1.5443802165 Simplifying x = 1.5443802165Subproblem 2
x + -0.5833333335 = -0.961046883 Simplifying x + -0.5833333335 = -0.961046883 Reorder the terms: -0.5833333335 + x = -0.961046883 Solving -0.5833333335 + x = -0.961046883 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 = -0.961046883 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.961046883 + 0.5833333335 x = -0.961046883 + 0.5833333335 Combine like terms: -0.961046883 + 0.5833333335 = -0.3777135495 x = -0.3777135495 Simplifying x = -0.3777135495Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5443802165, -0.3777135495}
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