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Simplifying 9x2 + -14x + -5 = 0 Reorder the terms: -5 + -14x + 9x2 = 0 Solving -5 + -14x + 9x2 = 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 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -1.555555556x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -1.555555556x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -1.555555556x + x2 = 0 + 0.5555555556 -1.555555556x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -1.555555556x + x2 = 0.5555555556 The x term is -1.555555556x. 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. -1.555555556x + 0.6049382720 + x2 = 0.5555555556 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = 0.5555555556 + 0.6049382720 Combine like terms: 0.5555555556 + 0.6049382720 = 1.1604938276 0.6049382720 + -1.555555556x + x2 = 1.1604938276 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 1.1604938276 Calculate the square root of the right side: 1.077262191 Break this problem into two subproblems by setting (x + -0.777777778) equal to 1.077262191 and -1.077262191.Subproblem 1
x + -0.777777778 = 1.077262191 Simplifying x + -0.777777778 = 1.077262191 Reorder the terms: -0.777777778 + x = 1.077262191 Solving -0.777777778 + x = 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 + x = 1.077262191 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 1.077262191 + 0.777777778 x = 1.077262191 + 0.777777778 Combine like terms: 1.077262191 + 0.777777778 = 1.855039969 x = 1.855039969 Simplifying x = 1.855039969Subproblem 2
x + -0.777777778 = -1.077262191 Simplifying x + -0.777777778 = -1.077262191 Reorder the terms: -0.777777778 + x = -1.077262191 Solving -0.777777778 + x = -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 + x = -1.077262191 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -1.077262191 + 0.777777778 x = -1.077262191 + 0.777777778 Combine like terms: -1.077262191 + 0.777777778 = -0.299484413 x = -0.299484413 Simplifying x = -0.299484413Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.855039969, -0.299484413}
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