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Simplifying 6x4 + -7x2 + -3 = 1 Reorder the terms: -3 + -7x2 + 6x4 = 1 Solving -3 + -7x2 + 6x4 = 1 Solving for variable 'x'. Reorder the terms: -3 + -1 + -7x2 + 6x4 = 1 + -1 Combine like terms: -3 + -1 = -4 -4 + -7x2 + 6x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -4 + -7x2 + 6x4 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.6666666667 + -1.166666667x2 + x4 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1.166666667x2 + 0.6666666667 + x4 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1.166666667x2 + x4 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1.166666667x2 + x4 = 0 + 0.6666666667 -1.166666667x2 + x4 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1.166666667x2 + x4 = 0.6666666667 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 = 0.6666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x2 + x4 = 0.6666666667 + 0.3402777780 Combine like terms: 0.6666666667 + 0.3402777780 = 1.0069444447 0.3402777780 + -1.166666667x2 + x4 = 1.0069444447 Factor a perfect square on the left side: (x2 + -0.5833333335)(x2 + -0.5833333335) = 1.0069444447 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x2 + -0.5833333335) equal to 1.003466215 and -1.003466215.Subproblem 1
x2 + -0.5833333335 = 1.003466215 Simplifying x2 + -0.5833333335 = 1.003466215 Reorder the terms: -0.5833333335 + x2 = 1.003466215 Solving -0.5833333335 + x2 = 1.003466215 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 = 1.003466215 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x2 = 1.003466215 + 0.5833333335 x2 = 1.003466215 + 0.5833333335 Combine like terms: 1.003466215 + 0.5833333335 = 1.5867995485 x2 = 1.5867995485 Simplifying x2 = 1.5867995485 Take the square root of each side: x = {-1.25968232, 1.25968232}Subproblem 2
x2 + -0.5833333335 = -1.003466215 Simplifying x2 + -0.5833333335 = -1.003466215 Reorder the terms: -0.5833333335 + x2 = -1.003466215 Solving -0.5833333335 + x2 = -1.003466215 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 = -1.003466215 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x2 = -1.003466215 + 0.5833333335 x2 = -1.003466215 + 0.5833333335 Combine like terms: -1.003466215 + 0.5833333335 = -0.4201328815 x2 = -0.4201328815 Simplifying x2 = -0.4201328815 Reorder the terms: 0.4201328815 + x2 = -0.4201328815 + 0.4201328815 Combine like terms: -0.4201328815 + 0.4201328815 = 0.0000000000 0.4201328815 + 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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