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Simplifying x4 + -16x2 + 49 = 0 Reorder the terms: 49 + -16x2 + x4 = 0 Solving 49 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -16x2 + -49 + x4 = 0 + -49 Reorder the terms: 49 + -49 + -16x2 + x4 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -16x2 + x4 = 0 + -49 -16x2 + x4 = 0 + -49 Combine like terms: 0 + -49 = -49 -16x2 + x4 = -49 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = -49 + 64 Reorder the terms: 64 + -16x2 + x4 = -49 + 64 Combine like terms: -49 + 64 = 15 64 + -16x2 + x4 = 15 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x2 + -8) equal to 3.872983346 and -3.872983346.Subproblem 1
x2 + -8 = 3.872983346 Simplifying x2 + -8 = 3.872983346 Reorder the terms: -8 + x2 = 3.872983346 Solving -8 + x2 = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 3.872983346 + 8 x2 = 3.872983346 + 8 Combine like terms: 3.872983346 + 8 = 11.872983346 x2 = 11.872983346 Simplifying x2 = 11.872983346 Take the square root of each side: x = {-3.445719569, 3.445719569}Subproblem 2
x2 + -8 = -3.872983346 Simplifying x2 + -8 = -3.872983346 Reorder the terms: -8 + x2 = -3.872983346 Solving -8 + x2 = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -3.872983346 + 8 x2 = -3.872983346 + 8 Combine like terms: -3.872983346 + 8 = 4.127016654 x2 = 4.127016654 Simplifying x2 = 4.127016654 Take the square root of each side: x = {-2.031506006, 2.031506006}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.445719569, 3.445719569, -2.031506006, 2.031506006}
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