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Simplifying x4 + 14x2 + 28.95 = 0 Reorder the terms: 28.95 + 14x2 + x4 = 0 Solving 28.95 + 14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-28.95' to each side of the equation. 28.95 + 14x2 + -28.95 + x4 = 0 + -28.95 Reorder the terms: 28.95 + -28.95 + 14x2 + x4 = 0 + -28.95 Combine like terms: 28.95 + -28.95 = 0.00 0.00 + 14x2 + x4 = 0 + -28.95 14x2 + x4 = 0 + -28.95 Combine like terms: 0 + -28.95 = -28.95 14x2 + x4 = -28.95 The x term is 14x2. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x2 + 49 + x4 = -28.95 + 49 Reorder the terms: 49 + 14x2 + x4 = -28.95 + 49 Combine like terms: -28.95 + 49 = 20.05 49 + 14x2 + x4 = 20.05 Factor a perfect square on the left side: (x2 + 7)(x2 + 7) = 20.05 Calculate the square root of the right side: 4.477722635 Break this problem into two subproblems by setting (x2 + 7) equal to 4.477722635 and -4.477722635.Subproblem 1
x2 + 7 = 4.477722635 Simplifying x2 + 7 = 4.477722635 Reorder the terms: 7 + x2 = 4.477722635 Solving 7 + x2 = 4.477722635 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 + x2 = 4.477722635 + -7 Combine like terms: 7 + -7 = 0 0 + x2 = 4.477722635 + -7 x2 = 4.477722635 + -7 Combine like terms: 4.477722635 + -7 = -2.522277365 x2 = -2.522277365 Simplifying x2 = -2.522277365 Reorder the terms: 2.522277365 + x2 = -2.522277365 + 2.522277365 Combine like terms: -2.522277365 + 2.522277365 = 0.000000000 2.522277365 + 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 + 7 = -4.477722635 Simplifying x2 + 7 = -4.477722635 Reorder the terms: 7 + x2 = -4.477722635 Solving 7 + x2 = -4.477722635 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 + x2 = -4.477722635 + -7 Combine like terms: 7 + -7 = 0 0 + x2 = -4.477722635 + -7 x2 = -4.477722635 + -7 Combine like terms: -4.477722635 + -7 = -11.477722635 x2 = -11.477722635 Simplifying x2 = -11.477722635 Reorder the terms: 11.477722635 + x2 = -11.477722635 + 11.477722635 Combine like terms: -11.477722635 + 11.477722635 = 0.000000000 11.477722635 + 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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