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Simplifying 64x4 + -320x2 + 1 = 0 Reorder the terms: 1 + -320x2 + 64x4 = 0 Solving 1 + -320x2 + 64x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.015625 + -5x2 + x4 = 0 Move the constant term to the right: Add '-0.015625' to each side of the equation. 0.015625 + -5x2 + -0.015625 + x4 = 0 + -0.015625 Reorder the terms: 0.015625 + -0.015625 + -5x2 + x4 = 0 + -0.015625 Combine like terms: 0.015625 + -0.015625 = 0.000000 0.000000 + -5x2 + x4 = 0 + -0.015625 -5x2 + x4 = 0 + -0.015625 Combine like terms: 0 + -0.015625 = -0.015625 -5x2 + x4 = -0.015625 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -0.015625 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -0.015625 + 6.25 Combine like terms: -0.015625 + 6.25 = 6.234375 6.25 + -5x2 + x4 = 6.234375 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 6.234375 Calculate the square root of the right side: 2.496873044 Break this problem into two subproblems by setting (x2 + -2.5) equal to 2.496873044 and -2.496873044.Subproblem 1
x2 + -2.5 = 2.496873044 Simplifying x2 + -2.5 = 2.496873044 Reorder the terms: -2.5 + x2 = 2.496873044 Solving -2.5 + x2 = 2.496873044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 2.496873044 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 2.496873044 + 2.5 x2 = 2.496873044 + 2.5 Combine like terms: 2.496873044 + 2.5 = 4.996873044 x2 = 4.996873044 Simplifying x2 = 4.996873044 Take the square root of each side: x = {-2.23536866, 2.23536866}Subproblem 2
x2 + -2.5 = -2.496873044 Simplifying x2 + -2.5 = -2.496873044 Reorder the terms: -2.5 + x2 = -2.496873044 Solving -2.5 + x2 = -2.496873044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -2.496873044 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -2.496873044 + 2.5 x2 = -2.496873044 + 2.5 Combine like terms: -2.496873044 + 2.5 = 0.003126956 x2 = 0.003126956 Simplifying x2 = 0.003126956 Take the square root of each side: x = {-0.055919192, 0.055919192}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.23536866, 2.23536866, -0.055919192, 0.055919192}
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