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Simplifying -2x2 + 11x = -29 Reorder the terms: 11x + -2x2 = -29 Solving 11x + -2x2 = -29 Solving for variable 'x'. Reorder the terms: 29 + 11x + -2x2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + 11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -14.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -5.5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -5.5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -5.5x + x2 = 0 + 14.5 -5.5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -5.5x + x2 = 14.5 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 = 14.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 14.5 + 7.5625 Combine like terms: 14.5 + 7.5625 = 22.0625 7.5625 + -5.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + -2.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + -2.75 = 4.697073557 Simplifying x + -2.75 = 4.697073557 Reorder the terms: -2.75 + x = 4.697073557 Solving -2.75 + x = 4.697073557 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 = 4.697073557 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 4.697073557 + 2.75 x = 4.697073557 + 2.75 Combine like terms: 4.697073557 + 2.75 = 7.447073557 x = 7.447073557 Simplifying x = 7.447073557Subproblem 2
x + -2.75 = -4.697073557 Simplifying x + -2.75 = -4.697073557 Reorder the terms: -2.75 + x = -4.697073557 Solving -2.75 + x = -4.697073557 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 = -4.697073557 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -4.697073557 + 2.75 x = -4.697073557 + 2.75 Combine like terms: -4.697073557 + 2.75 = -1.947073557 x = -1.947073557 Simplifying x = -1.947073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.447073557, -1.947073557}
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