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Simplifying x4 + -100x2 + 9 = 0 Reorder the terms: 9 + -100x2 + x4 = 0 Solving 9 + -100x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -100x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -100x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -100x2 + x4 = 0 + -9 -100x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -100x2 + x4 = -9 The x term is -100x2. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x2 + 2500 + x4 = -9 + 2500 Reorder the terms: 2500 + -100x2 + x4 = -9 + 2500 Combine like terms: -9 + 2500 = 2491 2500 + -100x2 + x4 = 2491 Factor a perfect square on the left side: (x2 + -50)(x2 + -50) = 2491 Calculate the square root of the right side: 49.909918854 Break this problem into two subproblems by setting (x2 + -50) equal to 49.909918854 and -49.909918854.Subproblem 1
x2 + -50 = 49.909918854 Simplifying x2 + -50 = 49.909918854 Reorder the terms: -50 + x2 = 49.909918854 Solving -50 + x2 = 49.909918854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x2 = 49.909918854 + 50 Combine like terms: -50 + 50 = 0 0 + x2 = 49.909918854 + 50 x2 = 49.909918854 + 50 Combine like terms: 49.909918854 + 50 = 99.909918854 x2 = 99.909918854 Simplifying x2 = 99.909918854 Take the square root of each side: x = {-9.995494928, 9.995494928}Subproblem 2
x2 + -50 = -49.909918854 Simplifying x2 + -50 = -49.909918854 Reorder the terms: -50 + x2 = -49.909918854 Solving -50 + x2 = -49.909918854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x2 = -49.909918854 + 50 Combine like terms: -50 + 50 = 0 0 + x2 = -49.909918854 + 50 x2 = -49.909918854 + 50 Combine like terms: -49.909918854 + 50 = 0.090081146 x2 = 0.090081146 Simplifying x2 = 0.090081146 Take the square root of each side: x = {-0.300135213, 0.300135213}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.995494928, 9.995494928, -0.300135213, 0.300135213}
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