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Simplifying x4 + -29x2 + -100 = 0 Reorder the terms: -100 + -29x2 + x4 = 0 Solving -100 + -29x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -29x2 + 100 + x4 = 0 + 100 Reorder the terms: -100 + 100 + -29x2 + x4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -29x2 + x4 = 0 + 100 -29x2 + x4 = 0 + 100 Combine like terms: 0 + 100 = 100 -29x2 + x4 = 100 The x term is -29x2. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x2 + 210.25 + x4 = 100 + 210.25 Reorder the terms: 210.25 + -29x2 + x4 = 100 + 210.25 Combine like terms: 100 + 210.25 = 310.25 210.25 + -29x2 + x4 = 310.25 Factor a perfect square on the left side: (x2 + -14.5)(x2 + -14.5) = 310.25 Calculate the square root of the right side: 17.613914954 Break this problem into two subproblems by setting (x2 + -14.5) equal to 17.613914954 and -17.613914954.Subproblem 1
x2 + -14.5 = 17.613914954 Simplifying x2 + -14.5 = 17.613914954 Reorder the terms: -14.5 + x2 = 17.613914954 Solving -14.5 + x2 = 17.613914954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x2 = 17.613914954 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x2 = 17.613914954 + 14.5 x2 = 17.613914954 + 14.5 Combine like terms: 17.613914954 + 14.5 = 32.113914954 x2 = 32.113914954 Simplifying x2 = 32.113914954 Take the square root of each side: x = {-5.666914059, 5.666914059}Subproblem 2
x2 + -14.5 = -17.613914954 Simplifying x2 + -14.5 = -17.613914954 Reorder the terms: -14.5 + x2 = -17.613914954 Solving -14.5 + x2 = -17.613914954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x2 = -17.613914954 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x2 = -17.613914954 + 14.5 x2 = -17.613914954 + 14.5 Combine like terms: -17.613914954 + 14.5 = -3.113914954 x2 = -3.113914954 Simplifying x2 = -3.113914954 Reorder the terms: 3.113914954 + x2 = -3.113914954 + 3.113914954 Combine like terms: -3.113914954 + 3.113914954 = 0.000000000 3.113914954 + 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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