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Simplifying x4 + 20x2 + -192 = 0 Reorder the terms: -192 + 20x2 + x4 = 0 Solving -192 + 20x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 20x2 + 192 + x4 = 0 + 192 Reorder the terms: -192 + 192 + 20x2 + x4 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 20x2 + x4 = 0 + 192 20x2 + x4 = 0 + 192 Combine like terms: 0 + 192 = 192 20x2 + x4 = 192 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 = 192 + 100 Reorder the terms: 100 + 20x2 + x4 = 192 + 100 Combine like terms: 192 + 100 = 292 100 + 20x2 + x4 = 292 Factor a perfect square on the left side: (x2 + 10)(x2 + 10) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x2 + 10) equal to 17.088007491 and -17.088007491.Subproblem 1
x2 + 10 = 17.088007491 Simplifying x2 + 10 = 17.088007491 Reorder the terms: 10 + x2 = 17.088007491 Solving 10 + x2 = 17.088007491 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 = 17.088007491 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = 17.088007491 + -10 x2 = 17.088007491 + -10 Combine like terms: 17.088007491 + -10 = 7.088007491 x2 = 7.088007491 Simplifying x2 = 7.088007491 Take the square root of each side: x = {-2.662331214, 2.662331214}Subproblem 2
x2 + 10 = -17.088007491 Simplifying x2 + 10 = -17.088007491 Reorder the terms: 10 + x2 = -17.088007491 Solving 10 + x2 = -17.088007491 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 = -17.088007491 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = -17.088007491 + -10 x2 = -17.088007491 + -10 Combine like terms: -17.088007491 + -10 = -27.088007491 x2 = -27.088007491 Simplifying x2 = -27.088007491 Reorder the terms: 27.088007491 + x2 = -27.088007491 + 27.088007491 Combine like terms: -27.088007491 + 27.088007491 = 0.000000000 27.088007491 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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