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Simplifying 100000x4 + -22050000x2 + 10000000 = 0 Reorder the terms: 10000000 + -22050000x2 + 100000x4 = 0 Solving 10000000 + -22050000x2 + 100000x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50000'. 50000(200 + -441x2 + 2x4) = 0 Ignore the factor 50000.Subproblem 1
Set the factor '(200 + -441x2 + 2x4)' equal to zero and attempt to solve: Simplifying 200 + -441x2 + 2x4 = 0 Solving 200 + -441x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 100 + -220.5x2 + x4 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -220.5x2 + -100 + x4 = 0 + -100 Reorder the terms: 100 + -100 + -220.5x2 + x4 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -220.5x2 + x4 = 0 + -100 -220.5x2 + x4 = 0 + -100 Combine like terms: 0 + -100 = -100 -220.5x2 + x4 = -100 The x term is -220.5x2. Take half its coefficient (-110.25). Square it (12155.0625) and add it to both sides. Add '12155.0625' to each side of the equation. -220.5x2 + 12155.0625 + x4 = -100 + 12155.0625 Reorder the terms: 12155.0625 + -220.5x2 + x4 = -100 + 12155.0625 Combine like terms: -100 + 12155.0625 = 12055.0625 12155.0625 + -220.5x2 + x4 = 12055.0625 Factor a perfect square on the left side: (x2 + -110.25)(x2 + -110.25) = 12055.0625 Calculate the square root of the right side: 109.795548635 Break this problem into two subproblems by setting (x2 + -110.25) equal to 109.795548635 and -109.795548635.Subproblem 1
x2 + -110.25 = 109.795548635 Simplifying x2 + -110.25 = 109.795548635 Reorder the terms: -110.25 + x2 = 109.795548635 Solving -110.25 + x2 = 109.795548635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110.25' to each side of the equation. -110.25 + 110.25 + x2 = 109.795548635 + 110.25 Combine like terms: -110.25 + 110.25 = 0.00 0.00 + x2 = 109.795548635 + 110.25 x2 = 109.795548635 + 110.25 Combine like terms: 109.795548635 + 110.25 = 220.045548635 x2 = 220.045548635 Simplifying x2 = 220.045548635 Take the square root of each side: x = {-14.833932339, 14.833932339}Subproblem 2
x2 + -110.25 = -109.795548635 Simplifying x2 + -110.25 = -109.795548635 Reorder the terms: -110.25 + x2 = -109.795548635 Solving -110.25 + x2 = -109.795548635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110.25' to each side of the equation. -110.25 + 110.25 + x2 = -109.795548635 + 110.25 Combine like terms: -110.25 + 110.25 = 0.00 0.00 + x2 = -109.795548635 + 110.25 x2 = -109.795548635 + 110.25 Combine like terms: -109.795548635 + 110.25 = 0.454451365 x2 = 0.454451365 Simplifying x2 = 0.454451365 Take the square root of each side: x = {-0.67413008, 0.67413008}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.833932339, 14.833932339, -0.67413008, 0.67413008}Solution
x = {-14.833932339, 14.833932339, -0.67413008, 0.67413008}
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