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Simplifying x4 + -26x2 + -15 = 0 Reorder the terms: -15 + -26x2 + x4 = 0 Solving -15 + -26x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -26x2 + 15 + x4 = 0 + 15 Reorder the terms: -15 + 15 + -26x2 + x4 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -26x2 + x4 = 0 + 15 -26x2 + x4 = 0 + 15 Combine like terms: 0 + 15 = 15 -26x2 + x4 = 15 The x term is -26x2. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x2 + 169 + x4 = 15 + 169 Reorder the terms: 169 + -26x2 + x4 = 15 + 169 Combine like terms: 15 + 169 = 184 169 + -26x2 + x4 = 184 Factor a perfect square on the left side: (x2 + -13)(x2 + -13) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x2 + -13) equal to 13.564659966 and -13.564659966.Subproblem 1
x2 + -13 = 13.564659966 Simplifying x2 + -13 = 13.564659966 Reorder the terms: -13 + x2 = 13.564659966 Solving -13 + x2 = 13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = 13.564659966 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = 13.564659966 + 13 x2 = 13.564659966 + 13 Combine like terms: 13.564659966 + 13 = 26.564659966 x2 = 26.564659966 Simplifying x2 = 26.564659966 Take the square root of each side: x = {-5.154091575, 5.154091575}Subproblem 2
x2 + -13 = -13.564659966 Simplifying x2 + -13 = -13.564659966 Reorder the terms: -13 + x2 = -13.564659966 Solving -13 + x2 = -13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = -13.564659966 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = -13.564659966 + 13 x2 = -13.564659966 + 13 Combine like terms: -13.564659966 + 13 = -0.564659966 x2 = -0.564659966 Simplifying x2 = -0.564659966 Reorder the terms: 0.564659966 + x2 = -0.564659966 + 0.564659966 Combine like terms: -0.564659966 + 0.564659966 = 0.000000000 0.564659966 + 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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