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Simplifying x4 + -134x2 + 125 = 0 Reorder the terms: 125 + -134x2 + x4 = 0 Solving 125 + -134x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + -134x2 + -125 + x4 = 0 + -125 Reorder the terms: 125 + -125 + -134x2 + x4 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -134x2 + x4 = 0 + -125 -134x2 + x4 = 0 + -125 Combine like terms: 0 + -125 = -125 -134x2 + x4 = -125 The x term is -134x2. Take half its coefficient (-67). Square it (4489) and add it to both sides. Add '4489' to each side of the equation. -134x2 + 4489 + x4 = -125 + 4489 Reorder the terms: 4489 + -134x2 + x4 = -125 + 4489 Combine like terms: -125 + 4489 = 4364 4489 + -134x2 + x4 = 4364 Factor a perfect square on the left side: (x2 + -67)(x2 + -67) = 4364 Calculate the square root of the right side: 66.06057826 Break this problem into two subproblems by setting (x2 + -67) equal to 66.06057826 and -66.06057826.Subproblem 1
x2 + -67 = 66.06057826 Simplifying x2 + -67 = 66.06057826 Reorder the terms: -67 + x2 = 66.06057826 Solving -67 + x2 = 66.06057826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + x2 = 66.06057826 + 67 Combine like terms: -67 + 67 = 0 0 + x2 = 66.06057826 + 67 x2 = 66.06057826 + 67 Combine like terms: 66.06057826 + 67 = 133.06057826 x2 = 133.06057826 Simplifying x2 = 133.06057826 Take the square root of each side: x = {-11.535188696, 11.535188696}Subproblem 2
x2 + -67 = -66.06057826 Simplifying x2 + -67 = -66.06057826 Reorder the terms: -67 + x2 = -66.06057826 Solving -67 + x2 = -66.06057826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + x2 = -66.06057826 + 67 Combine like terms: -67 + 67 = 0 0 + x2 = -66.06057826 + 67 x2 = -66.06057826 + 67 Combine like terms: -66.06057826 + 67 = 0.93942174 x2 = 0.93942174 Simplifying x2 = 0.93942174 Take the square root of each side: x = {-0.969237711, 0.969237711}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-11.535188696, 11.535188696, -0.969237711, 0.969237711}
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