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Simplifying x8 + 14x4 + -16 = 0 Reorder the terms: -16 + 14x4 + x8 = 0 Solving -16 + 14x4 + x8 = 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 + 14x4 + 16 + x8 = 0 + 16 Reorder the terms: -16 + 16 + 14x4 + x8 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 14x4 + x8 = 0 + 16 14x4 + x8 = 0 + 16 Combine like terms: 0 + 16 = 16 14x4 + x8 = 16 The x term is 14x4. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x4 + 49 + x8 = 16 + 49 Reorder the terms: 49 + 14x4 + x8 = 16 + 49 Combine like terms: 16 + 49 = 65 49 + 14x4 + x8 = 65 Factor a perfect square on the left side: (x4 + 7)(x4 + 7) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x4 + 7) equal to 8.062257748 and -8.062257748.Subproblem 1
x4 + 7 = 8.062257748 Simplifying x4 + 7 = 8.062257748 Reorder the terms: 7 + x4 = 8.062257748 Solving 7 + x4 = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x4 = 8.062257748 + -7 Combine like terms: 7 + -7 = 0 0 + x4 = 8.062257748 + -7 x4 = 8.062257748 + -7 Combine like terms: 8.062257748 + -7 = 1.062257748 x4 = 1.062257748 Simplifying x4 = 1.062257748 Reorder the terms: -1.062257748 + x4 = 1.062257748 + -1.062257748 Combine like terms: 1.062257748 + -1.062257748 = 0.000000000 -1.062257748 + x4 = 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
x4 + 7 = -8.062257748 Simplifying x4 + 7 = -8.062257748 Reorder the terms: 7 + x4 = -8.062257748 Solving 7 + x4 = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x4 = -8.062257748 + -7 Combine like terms: 7 + -7 = 0 0 + x4 = -8.062257748 + -7 x4 = -8.062257748 + -7 Combine like terms: -8.062257748 + -7 = -15.062257748 x4 = -15.062257748 Simplifying x4 = -15.062257748 Reorder the terms: 15.062257748 + x4 = -15.062257748 + 15.062257748 Combine like terms: -15.062257748 + 15.062257748 = 0.000000000 15.062257748 + x4 = 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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