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Simplifying 1 + 7x2 + -6x4 = 0 Solving 1 + 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'. -0.1666666667 + -1.166666667x2 + x4 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.166666667x2 + 0.1666666667 + x4 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.166666667x2 + x4 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.166666667x2 + x4 = 0 + 0.1666666667 -1.166666667x2 + x4 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.166666667x2 + x4 = 0.1666666667 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 = 0.1666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x2 + x4 = 0.1666666667 + 0.3402777780 Combine like terms: 0.1666666667 + 0.3402777780 = 0.5069444447 0.3402777780 + -1.166666667x2 + x4 = 0.5069444447 Factor a perfect square on the left side: (x2 + -0.5833333335)(x2 + -0.5833333335) = 0.5069444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (x2 + -0.5833333335) equal to 0.712000312 and -0.712000312.Subproblem 1
x2 + -0.5833333335 = 0.712000312 Simplifying x2 + -0.5833333335 = 0.712000312 Reorder the terms: -0.5833333335 + x2 = 0.712000312 Solving -0.5833333335 + x2 = 0.712000312 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 = 0.712000312 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x2 = 0.712000312 + 0.5833333335 x2 = 0.712000312 + 0.5833333335 Combine like terms: 0.712000312 + 0.5833333335 = 1.2953336455 x2 = 1.2953336455 Simplifying x2 = 1.2953336455 Take the square root of each side: x = {-1.138127254, 1.138127254}Subproblem 2
x2 + -0.5833333335 = -0.712000312 Simplifying x2 + -0.5833333335 = -0.712000312 Reorder the terms: -0.5833333335 + x2 = -0.712000312 Solving -0.5833333335 + x2 = -0.712000312 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 = -0.712000312 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x2 = -0.712000312 + 0.5833333335 x2 = -0.712000312 + 0.5833333335 Combine like terms: -0.712000312 + 0.5833333335 = -0.1286669785 x2 = -0.1286669785 Simplifying x2 = -0.1286669785 Reorder the terms: 0.1286669785 + x2 = -0.1286669785 + 0.1286669785 Combine like terms: -0.1286669785 + 0.1286669785 = 0.0000000000 0.1286669785 + 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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