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Simplifying x4 + -3.5x2 + 1 = 0 Reorder the terms: 1 + -3.5x2 + x4 = 0 Solving 1 + -3.5x2 + 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 + -3.5x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -3.5x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.5x2 + x4 = 0 + -1 -3.5x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.5x2 + x4 = -1 The x term is -3.5x2. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x2 + 3.0625 + x4 = -1 + 3.0625 Reorder the terms: 3.0625 + -3.5x2 + x4 = -1 + 3.0625 Combine like terms: -1 + 3.0625 = 2.0625 3.0625 + -3.5x2 + x4 = 2.0625 Factor a perfect square on the left side: (x2 + -1.75)(x2 + -1.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x2 + -1.75) equal to 1.436140662 and -1.436140662.Subproblem 1
x2 + -1.75 = 1.436140662 Simplifying x2 + -1.75 = 1.436140662 Reorder the terms: -1.75 + x2 = 1.436140662 Solving -1.75 + x2 = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x2 = 1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x2 = 1.436140662 + 1.75 x2 = 1.436140662 + 1.75 Combine like terms: 1.436140662 + 1.75 = 3.186140662 x2 = 3.186140662 Simplifying x2 = 3.186140662 Take the square root of each side: x = {-1.784976376, 1.784976376}Subproblem 2
x2 + -1.75 = -1.436140662 Simplifying x2 + -1.75 = -1.436140662 Reorder the terms: -1.75 + x2 = -1.436140662 Solving -1.75 + x2 = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x2 = -1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x2 = -1.436140662 + 1.75 x2 = -1.436140662 + 1.75 Combine like terms: -1.436140662 + 1.75 = 0.313859338 x2 = 0.313859338 Simplifying x2 = 0.313859338 Take the square root of each side: x = {-0.560231504, 0.560231504}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.784976376, 1.784976376, -0.560231504, 0.560231504}
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