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Simplifying x4 + -13x2 + 4 = 0 Reorder the terms: 4 + -13x2 + x4 = 0 Solving 4 + -13x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -13x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -13x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -13x2 + x4 = 0 + -4 -13x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -13x2 + x4 = -4 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 = -4 + 42.25 Reorder the terms: 42.25 + -13x2 + x4 = -4 + 42.25 Combine like terms: -4 + 42.25 = 38.25 42.25 + -13x2 + x4 = 38.25 Factor a perfect square on the left side: (x2 + -6.5)(x2 + -6.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x2 + -6.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x2 + -6.5 = 6.184658438 Simplifying x2 + -6.5 = 6.184658438 Reorder the terms: -6.5 + x2 = 6.184658438 Solving -6.5 + x2 = 6.184658438 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 = 6.184658438 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = 6.184658438 + 6.5 x2 = 6.184658438 + 6.5 Combine like terms: 6.184658438 + 6.5 = 12.684658438 x2 = 12.684658438 Simplifying x2 = 12.684658438 Take the square root of each side: x = {-3.561552813, 3.561552813}Subproblem 2
x2 + -6.5 = -6.184658438 Simplifying x2 + -6.5 = -6.184658438 Reorder the terms: -6.5 + x2 = -6.184658438 Solving -6.5 + x2 = -6.184658438 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 = -6.184658438 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = -6.184658438 + 6.5 x2 = -6.184658438 + 6.5 Combine like terms: -6.184658438 + 6.5 = 0.315341562 x2 = 0.315341562 Simplifying x2 = 0.315341562 Take the square root of each side: x = {-0.561552813, 0.561552813}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.561552813, 3.561552813, -0.561552813, 0.561552813}
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