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Simplifying x4 + 9x2 + 7 = 0 Reorder the terms: 7 + 9x2 + x4 = 0 Solving 7 + 9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 9x2 + -7 + x4 = 0 + -7 Reorder the terms: 7 + -7 + 9x2 + x4 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9x2 + x4 = 0 + -7 9x2 + x4 = 0 + -7 Combine like terms: 0 + -7 = -7 9x2 + x4 = -7 The x term is 9x2. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x2 + 20.25 + x4 = -7 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = -7 + 20.25 Combine like terms: -7 + 20.25 = 13.25 20.25 + 9x2 + x4 = 13.25 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x2 + 4.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x2 + 4.5 = 3.640054945 Simplifying x2 + 4.5 = 3.640054945 Reorder the terms: 4.5 + x2 = 3.640054945 Solving 4.5 + x2 = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = 3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 3.640054945 + -4.5 x2 = 3.640054945 + -4.5 Combine like terms: 3.640054945 + -4.5 = -0.859945055 x2 = -0.859945055 Simplifying x2 = -0.859945055 Reorder the terms: 0.859945055 + x2 = -0.859945055 + 0.859945055 Combine like terms: -0.859945055 + 0.859945055 = 0.000000000 0.859945055 + 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 + 4.5 = -3.640054945 Simplifying x2 + 4.5 = -3.640054945 Reorder the terms: 4.5 + x2 = -3.640054945 Solving 4.5 + x2 = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = -3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -3.640054945 + -4.5 x2 = -3.640054945 + -4.5 Combine like terms: -3.640054945 + -4.5 = -8.140054945 x2 = -8.140054945 Simplifying x2 = -8.140054945 Reorder the terms: 8.140054945 + x2 = -8.140054945 + 8.140054945 Combine like terms: -8.140054945 + 8.140054945 = 0.000000000 8.140054945 + 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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