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Simplifying x4 + 5x2 + -7 = 0 Reorder the terms: -7 + 5x2 + x4 = 0 Solving -7 + 5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 5x2 + 7 + x4 = 0 + 7 Reorder the terms: -7 + 7 + 5x2 + x4 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5x2 + x4 = 0 + 7 5x2 + x4 = 0 + 7 Combine like terms: 0 + 7 = 7 5x2 + x4 = 7 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = 7 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + 5x2 + x4 = 13.25 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x2 + 2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x2 + 2.5 = 3.640054945 Simplifying x2 + 2.5 = 3.640054945 Reorder the terms: 2.5 + x2 = 3.640054945 Solving 2.5 + x2 = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 3.640054945 + -2.5 x2 = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 x2 = 1.140054945 Simplifying x2 = 1.140054945 Take the square root of each side: x = {-1.067733555, 1.067733555}Subproblem 2
x2 + 2.5 = -3.640054945 Simplifying x2 + 2.5 = -3.640054945 Reorder the terms: 2.5 + x2 = -3.640054945 Solving 2.5 + x2 = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -3.640054945 + -2.5 x2 = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 x2 = -6.140054945 Simplifying x2 = -6.140054945 Reorder the terms: 6.140054945 + x2 = -6.140054945 + 6.140054945 Combine like terms: -6.140054945 + 6.140054945 = 0.000000000 6.140054945 + 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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