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Simplifying x4 + -20x2 + 16 = 0 Reorder the terms: 16 + -20x2 + x4 = 0 Solving 16 + -20x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -20x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + -20x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -20x2 + x4 = 0 + -16 -20x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 -20x2 + x4 = -16 The x term is -20x2. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x2 + 100 + x4 = -16 + 100 Reorder the terms: 100 + -20x2 + x4 = -16 + 100 Combine like terms: -16 + 100 = 84 100 + -20x2 + x4 = 84 Factor a perfect square on the left side: (x2 + -10)(x2 + -10) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x2 + -10) equal to 9.16515139 and -9.16515139.Subproblem 1
x2 + -10 = 9.16515139 Simplifying x2 + -10 = 9.16515139 Reorder the terms: -10 + x2 = 9.16515139 Solving -10 + x2 = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = 9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 9.16515139 + 10 x2 = 9.16515139 + 10 Combine like terms: 9.16515139 + 10 = 19.16515139 x2 = 19.16515139 Simplifying x2 = 19.16515139 Take the square root of each side: x = {-4.377802119, 4.377802119}Subproblem 2
x2 + -10 = -9.16515139 Simplifying x2 + -10 = -9.16515139 Reorder the terms: -10 + x2 = -9.16515139 Solving -10 + x2 = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = -9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -9.16515139 + 10 x2 = -9.16515139 + 10 Combine like terms: -9.16515139 + 10 = 0.83484861 x2 = 0.83484861 Simplifying x2 = 0.83484861 Take the square root of each side: x = {-0.913700503, 0.913700503}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.377802119, 4.377802119, -0.913700503, 0.913700503}
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