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Simplifying 9x4 + 14x2 + -5 = 0 Reorder the terms: -5 + 14x2 + 9x4 = 0 Solving -5 + 14x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 1.555555556x2 + x4 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 1.555555556x2 + 0.5555555556 + x4 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 1.555555556x2 + x4 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 1.555555556x2 + x4 = 0 + 0.5555555556 1.555555556x2 + x4 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 1.555555556x2 + x4 = 0.5555555556 The x term is 1.555555556x2. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x2 + 0.6049382720 + x4 = 0.5555555556 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x2 + x4 = 0.5555555556 + 0.6049382720 Combine like terms: 0.5555555556 + 0.6049382720 = 1.1604938276 0.6049382720 + 1.555555556x2 + x4 = 1.1604938276 Factor a perfect square on the left side: (x2 + 0.777777778)(x2 + 0.777777778) = 1.1604938276 Calculate the square root of the right side: 1.077262191 Break this problem into two subproblems by setting (x2 + 0.777777778) equal to 1.077262191 and -1.077262191.Subproblem 1
x2 + 0.777777778 = 1.077262191 Simplifying x2 + 0.777777778 = 1.077262191 Reorder the terms: 0.777777778 + x2 = 1.077262191 Solving 0.777777778 + x2 = 1.077262191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x2 = 1.077262191 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x2 = 1.077262191 + -0.777777778 x2 = 1.077262191 + -0.777777778 Combine like terms: 1.077262191 + -0.777777778 = 0.299484413 x2 = 0.299484413 Simplifying x2 = 0.299484413 Take the square root of each side: x = {-0.547251691, 0.547251691}Subproblem 2
x2 + 0.777777778 = -1.077262191 Simplifying x2 + 0.777777778 = -1.077262191 Reorder the terms: 0.777777778 + x2 = -1.077262191 Solving 0.777777778 + x2 = -1.077262191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x2 = -1.077262191 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x2 = -1.077262191 + -0.777777778 x2 = -1.077262191 + -0.777777778 Combine like terms: -1.077262191 + -0.777777778 = -1.855039969 x2 = -1.855039969 Simplifying x2 = -1.855039969 Reorder the terms: 1.855039969 + x2 = -1.855039969 + 1.855039969 Combine like terms: -1.855039969 + 1.855039969 = 0.000000000 1.855039969 + 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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