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Simplifying -2x2 + 9x + 29 = 0 Reorder the terms: 29 + 9x + -2x2 = 0 Solving 29 + 9x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -14.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -4.5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -4.5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -4.5x + x2 = 0 + 14.5 -4.5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -4.5x + x2 = 14.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 14.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 14.5 + 5.0625 Combine like terms: 14.5 + 5.0625 = 19.5625 5.0625 + -4.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + -2.25) equal to 4.422951503 and -4.422951503.Subproblem 1
x + -2.25 = 4.422951503 Simplifying x + -2.25 = 4.422951503 Reorder the terms: -2.25 + x = 4.422951503 Solving -2.25 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 4.422951503 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 4.422951503 + 2.25 x = 4.422951503 + 2.25 Combine like terms: 4.422951503 + 2.25 = 6.672951503 x = 6.672951503 Simplifying x = 6.672951503Subproblem 2
x + -2.25 = -4.422951503 Simplifying x + -2.25 = -4.422951503 Reorder the terms: -2.25 + x = -4.422951503 Solving -2.25 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -4.422951503 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -4.422951503 + 2.25 x = -4.422951503 + 2.25 Combine like terms: -4.422951503 + 2.25 = -2.172951503 x = -2.172951503 Simplifying x = -2.172951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.672951503, -2.172951503}
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