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Simplifying 8x4 + -8x2 + 1 = 0 Reorder the terms: 1 + -8x2 + 8x4 = 0 Solving 1 + -8x2 + 8x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -1x2 + x4 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1x2 + -0.125 + x4 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1x2 + x4 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1x2 + x4 = 0 + -0.125 -1x2 + x4 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1x2 + x4 = -0.125 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = -0.125 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = -0.125 + 0.25 Combine like terms: -0.125 + 0.25 = 0.125 0.25 + -1x2 + x4 = 0.125 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.353553391 and -0.353553391.Subproblem 1
x2 + -0.5 = 0.353553391 Simplifying x2 + -0.5 = 0.353553391 Reorder the terms: -0.5 + x2 = 0.353553391 Solving -0.5 + x2 = 0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 0.353553391 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.353553391 + 0.5 x2 = 0.353553391 + 0.5 Combine like terms: 0.353553391 + 0.5 = 0.853553391 x2 = 0.853553391 Simplifying x2 = 0.853553391 Take the square root of each side: x = {-0.923879533, 0.923879533}Subproblem 2
x2 + -0.5 = -0.353553391 Simplifying x2 + -0.5 = -0.353553391 Reorder the terms: -0.5 + x2 = -0.353553391 Solving -0.5 + x2 = -0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -0.353553391 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.353553391 + 0.5 x2 = -0.353553391 + 0.5 Combine like terms: -0.353553391 + 0.5 = 0.146446609 x2 = 0.146446609 Simplifying x2 = 0.146446609 Take the square root of each side: x = {-0.382683432, 0.382683432}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.923879533, 0.923879533, -0.382683432, 0.382683432}
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