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Simplifying x4 + -1.9984x2 + -3 = 0 Reorder the terms: -3 + -1.9984x2 + x4 = 0 Solving -3 + -1.9984x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.9984x2 + 3 + x4 = 0 + 3 Reorder the terms: -3 + 3 + -1.9984x2 + x4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.9984x2 + x4 = 0 + 3 -1.9984x2 + x4 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.9984x2 + x4 = 3 The x term is -1.9984x2. Take half its coefficient (-0.9992). Square it (0.99840064) and add it to both sides. Add '0.99840064' to each side of the equation. -1.9984x2 + 0.99840064 + x4 = 3 + 0.99840064 Reorder the terms: 0.99840064 + -1.9984x2 + x4 = 3 + 0.99840064 Combine like terms: 3 + 0.99840064 = 3.99840064 0.99840064 + -1.9984x2 + x4 = 3.99840064 Factor a perfect square on the left side: (x2 + -0.9992)(x2 + -0.9992) = 3.99840064 Calculate the square root of the right side: 1.99960012 Break this problem into two subproblems by setting (x2 + -0.9992) equal to 1.99960012 and -1.99960012.Subproblem 1
x2 + -0.9992 = 1.99960012 Simplifying x2 + -0.9992 = 1.99960012 Reorder the terms: -0.9992 + x2 = 1.99960012 Solving -0.9992 + x2 = 1.99960012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9992' to each side of the equation. -0.9992 + 0.9992 + x2 = 1.99960012 + 0.9992 Combine like terms: -0.9992 + 0.9992 = 0.0000 0.0000 + x2 = 1.99960012 + 0.9992 x2 = 1.99960012 + 0.9992 Combine like terms: 1.99960012 + 0.9992 = 2.99880012 x2 = 2.99880012 Simplifying x2 = 2.99880012 Take the square root of each side: x = {-1.731704397, 1.731704397}Subproblem 2
x2 + -0.9992 = -1.99960012 Simplifying x2 + -0.9992 = -1.99960012 Reorder the terms: -0.9992 + x2 = -1.99960012 Solving -0.9992 + x2 = -1.99960012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9992' to each side of the equation. -0.9992 + 0.9992 + x2 = -1.99960012 + 0.9992 Combine like terms: -0.9992 + 0.9992 = 0.0000 0.0000 + x2 = -1.99960012 + 0.9992 x2 = -1.99960012 + 0.9992 Combine like terms: -1.99960012 + 0.9992 = -1.00040012 x2 = -1.00040012 Simplifying x2 = -1.00040012 Reorder the terms: 1.00040012 + x2 = -1.00040012 + 1.00040012 Combine like terms: -1.00040012 + 1.00040012 = 0.00000000 1.00040012 + x2 = 0.00000000 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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