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Simplifying x4 + -25x2 + 135 = 0 Reorder the terms: 135 + -25x2 + x4 = 0 Solving 135 + -25x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-135' to each side of the equation. 135 + -25x2 + -135 + x4 = 0 + -135 Reorder the terms: 135 + -135 + -25x2 + x4 = 0 + -135 Combine like terms: 135 + -135 = 0 0 + -25x2 + x4 = 0 + -135 -25x2 + x4 = 0 + -135 Combine like terms: 0 + -135 = -135 -25x2 + x4 = -135 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 = -135 + 156.25 Reorder the terms: 156.25 + -25x2 + x4 = -135 + 156.25 Combine like terms: -135 + 156.25 = 21.25 156.25 + -25x2 + x4 = 21.25 Factor a perfect square on the left side: (x2 + -12.5)(x2 + -12.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x2 + -12.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x2 + -12.5 = 4.609772229 Simplifying x2 + -12.5 = 4.609772229 Reorder the terms: -12.5 + x2 = 4.609772229 Solving -12.5 + x2 = 4.609772229 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 = 4.609772229 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x2 = 4.609772229 + 12.5 x2 = 4.609772229 + 12.5 Combine like terms: 4.609772229 + 12.5 = 17.109772229 x2 = 17.109772229 Simplifying x2 = 17.109772229 Take the square root of each side: x = {-4.136396044, 4.136396044}Subproblem 2
x2 + -12.5 = -4.609772229 Simplifying x2 + -12.5 = -4.609772229 Reorder the terms: -12.5 + x2 = -4.609772229 Solving -12.5 + x2 = -4.609772229 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 = -4.609772229 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x2 = -4.609772229 + 12.5 x2 = -4.609772229 + 12.5 Combine like terms: -4.609772229 + 12.5 = 7.890227771 x2 = 7.890227771 Simplifying x2 = 7.890227771 Take the square root of each side: x = {-2.808954925, 2.808954925}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.136396044, 4.136396044, -2.808954925, 2.808954925}
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