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Simplifying x4 + -6x2 + -53 = 0 Reorder the terms: -53 + -6x2 + x4 = 0 Solving -53 + -6x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -6x2 + 53 + x4 = 0 + 53 Reorder the terms: -53 + 53 + -6x2 + x4 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -6x2 + x4 = 0 + 53 -6x2 + x4 = 0 + 53 Combine like terms: 0 + 53 = 53 -6x2 + x4 = 53 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = 53 + 9 Reorder the terms: 9 + -6x2 + x4 = 53 + 9 Combine like terms: 53 + 9 = 62 9 + -6x2 + x4 = 62 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x2 + -3) equal to 7.874007874 and -7.874007874.Subproblem 1
x2 + -3 = 7.874007874 Simplifying x2 + -3 = 7.874007874 Reorder the terms: -3 + x2 = 7.874007874 Solving -3 + x2 = 7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 7.874007874 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 7.874007874 + 3 x2 = 7.874007874 + 3 Combine like terms: 7.874007874 + 3 = 10.874007874 x2 = 10.874007874 Simplifying x2 = 10.874007874 Take the square root of each side: x = {-3.29757606, 3.29757606}Subproblem 2
x2 + -3 = -7.874007874 Simplifying x2 + -3 = -7.874007874 Reorder the terms: -3 + x2 = -7.874007874 Solving -3 + x2 = -7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -7.874007874 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -7.874007874 + 3 x2 = -7.874007874 + 3 Combine like terms: -7.874007874 + 3 = -4.874007874 x2 = -4.874007874 Simplifying x2 = -4.874007874 Reorder the terms: 4.874007874 + x2 = -4.874007874 + 4.874007874 Combine like terms: -4.874007874 + 4.874007874 = 0.000000000 4.874007874 + 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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