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Simplifying x4 + -6x2 + -55 = 15 Reorder the terms: -55 + -6x2 + x4 = 15 Solving -55 + -6x2 + x4 = 15 Solving for variable 'x'. Reorder the terms: -55 + -15 + -6x2 + x4 = 15 + -15 Combine like terms: -55 + -15 = -70 -70 + -6x2 + x4 = 15 + -15 Combine like terms: 15 + -15 = 0 -70 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -6x2 + 70 + x4 = 0 + 70 Reorder the terms: -70 + 70 + -6x2 + x4 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -6x2 + x4 = 0 + 70 -6x2 + x4 = 0 + 70 Combine like terms: 0 + 70 = 70 -6x2 + x4 = 70 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 = 70 + 9 Reorder the terms: 9 + -6x2 + x4 = 70 + 9 Combine like terms: 70 + 9 = 79 9 + -6x2 + x4 = 79 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x2 + -3) equal to 8.888194417 and -8.888194417.Subproblem 1
x2 + -3 = 8.888194417 Simplifying x2 + -3 = 8.888194417 Reorder the terms: -3 + x2 = 8.888194417 Solving -3 + x2 = 8.888194417 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 = 8.888194417 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 8.888194417 + 3 x2 = 8.888194417 + 3 Combine like terms: 8.888194417 + 3 = 11.888194417 x2 = 11.888194417 Simplifying x2 = 11.888194417 Take the square root of each side: x = {-3.447926104, 3.447926104}Subproblem 2
x2 + -3 = -8.888194417 Simplifying x2 + -3 = -8.888194417 Reorder the terms: -3 + x2 = -8.888194417 Solving -3 + x2 = -8.888194417 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 = -8.888194417 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -8.888194417 + 3 x2 = -8.888194417 + 3 Combine like terms: -8.888194417 + 3 = -5.888194417 x2 = -5.888194417 Simplifying x2 = -5.888194417 Reorder the terms: 5.888194417 + x2 = -5.888194417 + 5.888194417 Combine like terms: -5.888194417 + 5.888194417 = 0.000000000 5.888194417 + 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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