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Simplifying x4 + -42x2 + -59 = 0 Reorder the terms: -59 + -42x2 + x4 = 0 Solving -59 + -42x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + -42x2 + 59 + x4 = 0 + 59 Reorder the terms: -59 + 59 + -42x2 + x4 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -42x2 + x4 = 0 + 59 -42x2 + x4 = 0 + 59 Combine like terms: 0 + 59 = 59 -42x2 + x4 = 59 The x term is -42x2. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x2 + 441 + x4 = 59 + 441 Reorder the terms: 441 + -42x2 + x4 = 59 + 441 Combine like terms: 59 + 441 = 500 441 + -42x2 + x4 = 500 Factor a perfect square on the left side: (x2 + -21)(x2 + -21) = 500 Calculate the square root of the right side: 22.360679775 Break this problem into two subproblems by setting (x2 + -21) equal to 22.360679775 and -22.360679775.Subproblem 1
x2 + -21 = 22.360679775 Simplifying x2 + -21 = 22.360679775 Reorder the terms: -21 + x2 = 22.360679775 Solving -21 + x2 = 22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x2 = 22.360679775 + 21 Combine like terms: -21 + 21 = 0 0 + x2 = 22.360679775 + 21 x2 = 22.360679775 + 21 Combine like terms: 22.360679775 + 21 = 43.360679775 x2 = 43.360679775 Simplifying x2 = 43.360679775 Take the square root of each side: x = {-6.58488267, 6.58488267}Subproblem 2
x2 + -21 = -22.360679775 Simplifying x2 + -21 = -22.360679775 Reorder the terms: -21 + x2 = -22.360679775 Solving -21 + x2 = -22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x2 = -22.360679775 + 21 Combine like terms: -21 + 21 = 0 0 + x2 = -22.360679775 + 21 x2 = -22.360679775 + 21 Combine like terms: -22.360679775 + 21 = -1.360679775 x2 = -1.360679775 Simplifying x2 = -1.360679775 Reorder the terms: 1.360679775 + x2 = -1.360679775 + 1.360679775 Combine like terms: -1.360679775 + 1.360679775 = 0.000000000 1.360679775 + x2 = 0.000000000 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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