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Simplifying 4x4 + 11x2 + 3 = 0 Reorder the terms: 3 + 11x2 + 4x4 = 0 Solving 3 + 11x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 2.75x2 + x4 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 2.75x2 + -0.75 + x4 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 2.75x2 + x4 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 2.75x2 + x4 = 0 + -0.75 2.75x2 + x4 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 2.75x2 + x4 = -0.75 The x term is 2.75x2. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x2 + 1.890625 + x4 = -0.75 + 1.890625 Reorder the terms: 1.890625 + 2.75x2 + x4 = -0.75 + 1.890625 Combine like terms: -0.75 + 1.890625 = 1.140625 1.890625 + 2.75x2 + x4 = 1.140625 Factor a perfect square on the left side: (x2 + 1.375)(x2 + 1.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x2 + 1.375) equal to 1.068000468 and -1.068000468.Subproblem 1
x2 + 1.375 = 1.068000468 Simplifying x2 + 1.375 = 1.068000468 Reorder the terms: 1.375 + x2 = 1.068000468 Solving 1.375 + x2 = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x2 = 1.068000468 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x2 = 1.068000468 + -1.375 x2 = 1.068000468 + -1.375 Combine like terms: 1.068000468 + -1.375 = -0.306999532 x2 = -0.306999532 Simplifying x2 = -0.306999532 Reorder the terms: 0.306999532 + x2 = -0.306999532 + 0.306999532 Combine like terms: -0.306999532 + 0.306999532 = 0.000000000 0.306999532 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 1.375 = -1.068000468 Simplifying x2 + 1.375 = -1.068000468 Reorder the terms: 1.375 + x2 = -1.068000468 Solving 1.375 + x2 = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x2 = -1.068000468 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x2 = -1.068000468 + -1.375 x2 = -1.068000468 + -1.375 Combine like terms: -1.068000468 + -1.375 = -2.443000468 x2 = -2.443000468 Simplifying x2 = -2.443000468 Reorder the terms: 2.443000468 + x2 = -2.443000468 + 2.443000468 Combine like terms: -2.443000468 + 2.443000468 = 0.000000000 2.443000468 + 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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