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Simplifying x4 + -50x2 + 40 = 0 Reorder the terms: 40 + -50x2 + x4 = 0 Solving 40 + -50x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -50x2 + -40 + x4 = 0 + -40 Reorder the terms: 40 + -40 + -50x2 + x4 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -50x2 + x4 = 0 + -40 -50x2 + x4 = 0 + -40 Combine like terms: 0 + -40 = -40 -50x2 + x4 = -40 The x term is -50x2. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x2 + 625 + x4 = -40 + 625 Reorder the terms: 625 + -50x2 + x4 = -40 + 625 Combine like terms: -40 + 625 = 585 625 + -50x2 + x4 = 585 Factor a perfect square on the left side: (x2 + -25)(x2 + -25) = 585 Calculate the square root of the right side: 24.186773245 Break this problem into two subproblems by setting (x2 + -25) equal to 24.186773245 and -24.186773245.Subproblem 1
x2 + -25 = 24.186773245 Simplifying x2 + -25 = 24.186773245 Reorder the terms: -25 + x2 = 24.186773245 Solving -25 + x2 = 24.186773245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x2 = 24.186773245 + 25 Combine like terms: -25 + 25 = 0 0 + x2 = 24.186773245 + 25 x2 = 24.186773245 + 25 Combine like terms: 24.186773245 + 25 = 49.186773245 x2 = 49.186773245 Simplifying x2 = 49.186773245 Take the square root of each side: x = {-7.013328257, 7.013328257}Subproblem 2
x2 + -25 = -24.186773245 Simplifying x2 + -25 = -24.186773245 Reorder the terms: -25 + x2 = -24.186773245 Solving -25 + x2 = -24.186773245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x2 = -24.186773245 + 25 Combine like terms: -25 + 25 = 0 0 + x2 = -24.186773245 + 25 x2 = -24.186773245 + 25 Combine like terms: -24.186773245 + 25 = 0.813226755 x2 = 0.813226755 Simplifying x2 = 0.813226755 Take the square root of each side: x = {-0.90179086, 0.90179086}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.013328257, 7.013328257, -0.90179086, 0.90179086}
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