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Simplifying x4 + -15x2 + 16 = 0 Reorder the terms: 16 + -15x2 + x4 = 0 Solving 16 + -15x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -15x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + -15x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -15x2 + x4 = 0 + -16 -15x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 -15x2 + x4 = -16 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 = -16 + 56.25 Reorder the terms: 56.25 + -15x2 + x4 = -16 + 56.25 Combine like terms: -16 + 56.25 = 40.25 56.25 + -15x2 + x4 = 40.25 Factor a perfect square on the left side: (x2 + -7.5)(x2 + -7.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x2 + -7.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x2 + -7.5 = 6.34428877 Simplifying x2 + -7.5 = 6.34428877 Reorder the terms: -7.5 + x2 = 6.34428877 Solving -7.5 + x2 = 6.34428877 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 = 6.34428877 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 6.34428877 + 7.5 x2 = 6.34428877 + 7.5 Combine like terms: 6.34428877 + 7.5 = 13.84428877 x2 = 13.84428877 Simplifying x2 = 13.84428877 Take the square root of each side: x = {-3.720791417, 3.720791417}Subproblem 2
x2 + -7.5 = -6.34428877 Simplifying x2 + -7.5 = -6.34428877 Reorder the terms: -7.5 + x2 = -6.34428877 Solving -7.5 + x2 = -6.34428877 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 = -6.34428877 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -6.34428877 + 7.5 x2 = -6.34428877 + 7.5 Combine like terms: -6.34428877 + 7.5 = 1.15571123 x2 = 1.15571123 Simplifying x2 = 1.15571123 Take the square root of each side: x = {-1.075040106, 1.075040106}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.720791417, 3.720791417, -1.075040106, 1.075040106}
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