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Simplifying x4 + -13x2 + 38 = 0 Reorder the terms: 38 + -13x2 + x4 = 0 Solving 38 + -13x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + -13x2 + -38 + x4 = 0 + -38 Reorder the terms: 38 + -38 + -13x2 + x4 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -13x2 + x4 = 0 + -38 -13x2 + x4 = 0 + -38 Combine like terms: 0 + -38 = -38 -13x2 + x4 = -38 The x term is -13x2. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x2 + 42.25 + x4 = -38 + 42.25 Reorder the terms: 42.25 + -13x2 + x4 = -38 + 42.25 Combine like terms: -38 + 42.25 = 4.25 42.25 + -13x2 + x4 = 4.25 Factor a perfect square on the left side: (x2 + -6.5)(x2 + -6.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x2 + -6.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x2 + -6.5 = 2.061552813 Simplifying x2 + -6.5 = 2.061552813 Reorder the terms: -6.5 + x2 = 2.061552813 Solving -6.5 + x2 = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = 2.061552813 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = 2.061552813 + 6.5 x2 = 2.061552813 + 6.5 Combine like terms: 2.061552813 + 6.5 = 8.561552813 x2 = 8.561552813 Simplifying x2 = 8.561552813 Take the square root of each side: x = {-2.926013126, 2.926013126}Subproblem 2
x2 + -6.5 = -2.061552813 Simplifying x2 + -6.5 = -2.061552813 Reorder the terms: -6.5 + x2 = -2.061552813 Solving -6.5 + x2 = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = -2.061552813 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = -2.061552813 + 6.5 x2 = -2.061552813 + 6.5 Combine like terms: -2.061552813 + 6.5 = 4.438447187 x2 = 4.438447187 Simplifying x2 = 4.438447187 Take the square root of each side: x = {-2.106762252, 2.106762252}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.926013126, 2.926013126, -2.106762252, 2.106762252}
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