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Simplifying x4 + -15x2 + 35 = 0 Reorder the terms: 35 + -15x2 + x4 = 0 Solving 35 + -15x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -15x2 + -35 + x4 = 0 + -35 Reorder the terms: 35 + -35 + -15x2 + x4 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -15x2 + x4 = 0 + -35 -15x2 + x4 = 0 + -35 Combine like terms: 0 + -35 = -35 -15x2 + x4 = -35 The x term is -15x2. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x2 + 56.25 + x4 = -35 + 56.25 Reorder the terms: 56.25 + -15x2 + x4 = -35 + 56.25 Combine like terms: -35 + 56.25 = 21.25 56.25 + -15x2 + x4 = 21.25 Factor a perfect square on the left side: (x2 + -7.5)(x2 + -7.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x2 + -7.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x2 + -7.5 = 4.609772229 Simplifying x2 + -7.5 = 4.609772229 Reorder the terms: -7.5 + x2 = 4.609772229 Solving -7.5 + x2 = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = 4.609772229 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 4.609772229 + 7.5 x2 = 4.609772229 + 7.5 Combine like terms: 4.609772229 + 7.5 = 12.109772229 x2 = 12.109772229 Simplifying x2 = 12.109772229 Take the square root of each side: x = {-3.479909802, 3.479909802}Subproblem 2
x2 + -7.5 = -4.609772229 Simplifying x2 + -7.5 = -4.609772229 Reorder the terms: -7.5 + x2 = -4.609772229 Solving -7.5 + x2 = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = -4.609772229 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -4.609772229 + 7.5 x2 = -4.609772229 + 7.5 Combine like terms: -4.609772229 + 7.5 = 2.890227771 x2 = 2.890227771 Simplifying x2 = 2.890227771 Take the square root of each side: x = {-1.70006699, 1.70006699}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.479909802, 3.479909802, -1.70006699, 1.70006699}
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