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Simplifying x4 + -25x2 + 20 = 0 Reorder the terms: 20 + -25x2 + x4 = 0 Solving 20 + -25x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -25x2 + -20 + x4 = 0 + -20 Reorder the terms: 20 + -20 + -25x2 + x4 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -25x2 + x4 = 0 + -20 -25x2 + x4 = 0 + -20 Combine like terms: 0 + -20 = -20 -25x2 + x4 = -20 The x term is -25x2. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x2 + 156.25 + x4 = -20 + 156.25 Reorder the terms: 156.25 + -25x2 + x4 = -20 + 156.25 Combine like terms: -20 + 156.25 = 136.25 156.25 + -25x2 + x4 = 136.25 Factor a perfect square on the left side: (x2 + -12.5)(x2 + -12.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x2 + -12.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x2 + -12.5 = 11.67261753 Simplifying x2 + -12.5 = 11.67261753 Reorder the terms: -12.5 + x2 = 11.67261753 Solving -12.5 + x2 = 11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x2 = 11.67261753 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x2 = 11.67261753 + 12.5 x2 = 11.67261753 + 12.5 Combine like terms: 11.67261753 + 12.5 = 24.17261753 x2 = 24.17261753 Simplifying x2 = 24.17261753 Take the square root of each side: x = {-4.916565623, 4.916565623}Subproblem 2
x2 + -12.5 = -11.67261753 Simplifying x2 + -12.5 = -11.67261753 Reorder the terms: -12.5 + x2 = -11.67261753 Solving -12.5 + x2 = -11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x2 = -11.67261753 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x2 = -11.67261753 + 12.5 x2 = -11.67261753 + 12.5 Combine like terms: -11.67261753 + 12.5 = 0.82738247 x2 = 0.82738247 Simplifying x2 = 0.82738247 Take the square root of each side: x = {-0.909605667, 0.909605667}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.916565623, 4.916565623, -0.909605667, 0.909605667}
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