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Simplifying 6x4 + -7x2 + -2 = 0 Reorder the terms: -2 + -7x2 + 6x4 = 0 Solving -2 + -7x2 + 6x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + -1.166666667x2 + x4 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.166666667x2 + 0.3333333333 + x4 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.166666667x2 + x4 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.166666667x2 + x4 = 0 + 0.3333333333 -1.166666667x2 + x4 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.166666667x2 + x4 = 0.3333333333 The x term is -1.166666667x2. 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. -1.166666667x2 + 0.3402777780 + x4 = 0.3333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x2 + x4 = 0.3333333333 + 0.3402777780 Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113 0.3402777780 + -1.166666667x2 + x4 = 0.6736111113 Factor a perfect square on the left side: (x2 + -0.5833333335)(x2 + -0.5833333335) = 0.6736111113 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (x2 + -0.5833333335) equal to 0.82073815 and -0.82073815.Subproblem 1
x2 + -0.5833333335 = 0.82073815 Simplifying x2 + -0.5833333335 = 0.82073815 Reorder the terms: -0.5833333335 + x2 = 0.82073815 Solving -0.5833333335 + x2 = 0.82073815 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 + x2 = 0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x2 = 0.82073815 + 0.5833333335 x2 = 0.82073815 + 0.5833333335 Combine like terms: 0.82073815 + 0.5833333335 = 1.4040714835 x2 = 1.4040714835 Simplifying x2 = 1.4040714835 Take the square root of each side: x = {-1.184935223, 1.184935223}Subproblem 2
x2 + -0.5833333335 = -0.82073815 Simplifying x2 + -0.5833333335 = -0.82073815 Reorder the terms: -0.5833333335 + x2 = -0.82073815 Solving -0.5833333335 + x2 = -0.82073815 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 + x2 = -0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x2 = -0.82073815 + 0.5833333335 x2 = -0.82073815 + 0.5833333335 Combine like terms: -0.82073815 + 0.5833333335 = -0.2374048165 x2 = -0.2374048165 Simplifying x2 = -0.2374048165 Reorder the terms: 0.2374048165 + x2 = -0.2374048165 + 0.2374048165 Combine like terms: -0.2374048165 + 0.2374048165 = 0.0000000000 0.2374048165 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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