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Simplifying 0 = 9x2 + 14x + -5 Reorder the terms: 0 = -5 + 14x + 9x2 Solving 0 = -5 + 14x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -14x + -9x2 = -5 + 14x + 9x2 + 5 + -14x + -9x2 Reorder the terms: 5 + -14x + -9x2 = -5 + 5 + 14x + -14x + 9x2 + -9x2 Combine like terms: -5 + 5 = 0 5 + -14x + -9x2 = 0 + 14x + -14x + 9x2 + -9x2 5 + -14x + -9x2 = 14x + -14x + 9x2 + -9x2 Combine like terms: 14x + -14x = 0 5 + -14x + -9x2 = 0 + 9x2 + -9x2 5 + -14x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 5 + -14x + -9x2 = 0 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 = 0.299484413 x = 0.299484413 Simplifying x = 0.299484413Subproblem 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 = -1.855039969 x = -1.855039969 Simplifying x = -1.855039969Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.299484413, -1.855039969}
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