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Simplifying 0 = 2x2 + 11x + -24 Reorder the terms: 0 = -24 + 11x + 2x2 Solving 0 = -24 + 11x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + -11x + -2x2 = -24 + 11x + 2x2 + 24 + -11x + -2x2 Reorder the terms: 24 + -11x + -2x2 = -24 + 24 + 11x + -11x + 2x2 + -2x2 Combine like terms: -24 + 24 = 0 24 + -11x + -2x2 = 0 + 11x + -11x + 2x2 + -2x2 24 + -11x + -2x2 = 11x + -11x + 2x2 + -2x2 Combine like terms: 11x + -11x = 0 24 + -11x + -2x2 = 0 + 2x2 + -2x2 24 + -11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 24 + -11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12 + 5.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 5.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 5.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 5.5x + x2 = 0 + 12 5.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 5.5x + x2 = 12 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 12 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 12 + 7.5625 Combine like terms: 12 + 7.5625 = 19.5625 7.5625 + 5.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + 2.75) equal to 4.422951503 and -4.422951503.Subproblem 1
x + 2.75 = 4.422951503 Simplifying x + 2.75 = 4.422951503 Reorder the terms: 2.75 + x = 4.422951503 Solving 2.75 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.422951503 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.422951503 + -2.75 x = 4.422951503 + -2.75 Combine like terms: 4.422951503 + -2.75 = 1.672951503 x = 1.672951503 Simplifying x = 1.672951503Subproblem 2
x + 2.75 = -4.422951503 Simplifying x + 2.75 = -4.422951503 Reorder the terms: 2.75 + x = -4.422951503 Solving 2.75 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.422951503 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.422951503 + -2.75 x = -4.422951503 + -2.75 Combine like terms: -4.422951503 + -2.75 = -7.172951503 x = -7.172951503 Simplifying x = -7.172951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.672951503, -7.172951503}
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