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Simplifying x4 + -26x2 = 25 Reorder the terms: -26x2 + x4 = 25 Solving -26x2 + x4 = 25 Solving for variable 'x'. Reorder the terms: -25 + -26x2 + x4 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -26x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -26x2 + 25 + x4 = 0 + 25 Reorder the terms: -25 + 25 + -26x2 + x4 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -26x2 + x4 = 0 + 25 -26x2 + x4 = 0 + 25 Combine like terms: 0 + 25 = 25 -26x2 + x4 = 25 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 = 25 + 169 Reorder the terms: 169 + -26x2 + x4 = 25 + 169 Combine like terms: 25 + 169 = 194 169 + -26x2 + x4 = 194 Factor a perfect square on the left side: (x2 + -13)(x2 + -13) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (x2 + -13) equal to 13.928388277 and -13.928388277.Subproblem 1
x2 + -13 = 13.928388277 Simplifying x2 + -13 = 13.928388277 Reorder the terms: -13 + x2 = 13.928388277 Solving -13 + x2 = 13.928388277 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 = 13.928388277 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = 13.928388277 + 13 x2 = 13.928388277 + 13 Combine like terms: 13.928388277 + 13 = 26.928388277 x2 = 26.928388277 Simplifying x2 = 26.928388277 Take the square root of each side: x = {-5.189257006, 5.189257006}Subproblem 2
x2 + -13 = -13.928388277 Simplifying x2 + -13 = -13.928388277 Reorder the terms: -13 + x2 = -13.928388277 Solving -13 + x2 = -13.928388277 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 = -13.928388277 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = -13.928388277 + 13 x2 = -13.928388277 + 13 Combine like terms: -13.928388277 + 13 = -0.928388277 x2 = -0.928388277 Simplifying x2 = -0.928388277 Reorder the terms: 0.928388277 + x2 = -0.928388277 + 0.928388277 Combine like terms: -0.928388277 + 0.928388277 = 0.000000000 0.928388277 + 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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