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Simplifying x4 + -10x2 + 1 = 0 Reorder the terms: 1 + -10x2 + x4 = 0 Solving 1 + -10x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -10x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10x2 + x4 = 0 + -1 -10x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -10x2 + x4 = -1 The x term is -10x2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x2 + 25 + x4 = -1 + 25 Reorder the terms: 25 + -10x2 + x4 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + -10x2 + x4 = 24 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x2 + -5) equal to 4.898979486 and -4.898979486.Subproblem 1
x2 + -5 = 4.898979486 Simplifying x2 + -5 = 4.898979486 Reorder the terms: -5 + x2 = 4.898979486 Solving -5 + x2 = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 4.898979486 + 5 x2 = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 x2 = 9.898979486 Simplifying x2 = 9.898979486 Take the square root of each side: x = {-3.14626437, 3.14626437}Subproblem 2
x2 + -5 = -4.898979486 Simplifying x2 + -5 = -4.898979486 Reorder the terms: -5 + x2 = -4.898979486 Solving -5 + x2 = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -4.898979486 + 5 x2 = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 x2 = 0.101020514 Simplifying x2 = 0.101020514 Take the square root of each side: x = {-0.317837245, 0.317837245}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.14626437, 3.14626437, -0.317837245, 0.317837245}
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