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Simplifying X4 + -26X2 + -28 = 0 Reorder the terms: -28 + -26X2 + X4 = 0 Solving -28 + -26X2 + X4 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -26X2 + 28 + X4 = 0 + 28 Reorder the terms: -28 + 28 + -26X2 + X4 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -26X2 + X4 = 0 + 28 -26X2 + X4 = 0 + 28 Combine like terms: 0 + 28 = 28 -26X2 + X4 = 28 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 = 28 + 169 Reorder the terms: 169 + -26X2 + X4 = 28 + 169 Combine like terms: 28 + 169 = 197 169 + -26X2 + X4 = 197 Factor a perfect square on the left side: (X2 + -13)(X2 + -13) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (X2 + -13) equal to 14.035668848 and -14.035668848.Subproblem 1
X2 + -13 = 14.035668848 Simplifying X2 + -13 = 14.035668848 Reorder the terms: -13 + X2 = 14.035668848 Solving -13 + X2 = 14.035668848 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 = 14.035668848 + 13 Combine like terms: -13 + 13 = 0 0 + X2 = 14.035668848 + 13 X2 = 14.035668848 + 13 Combine like terms: 14.035668848 + 13 = 27.035668848 X2 = 27.035668848 Simplifying X2 = 27.035668848 Take the square root of each side: X = {-5.199583526, 5.199583526}Subproblem 2
X2 + -13 = -14.035668848 Simplifying X2 + -13 = -14.035668848 Reorder the terms: -13 + X2 = -14.035668848 Solving -13 + X2 = -14.035668848 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 = -14.035668848 + 13 Combine like terms: -13 + 13 = 0 0 + X2 = -14.035668848 + 13 X2 = -14.035668848 + 13 Combine like terms: -14.035668848 + 13 = -1.035668848 X2 = -1.035668848 Simplifying X2 = -1.035668848 Reorder the terms: 1.035668848 + X2 = -1.035668848 + 1.035668848 Combine like terms: -1.035668848 + 1.035668848 = 0.000000000 1.035668848 + 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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