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Simplifying (11 + 2x) * x = 63 * 63 Reorder the terms for easier multiplication: x(11 + 2x) = 63 * 63 (11 * x + 2x * x) = 63 * 63 (11x + 2x2) = 63 * 63 Multiply 63 * 63 11x + 2x2 = 3969 Solving 11x + 2x2 = 3969 Solving for variable 'x'. Reorder the terms: -3969 + 11x + 2x2 = 3969 + -3969 Combine like terms: 3969 + -3969 = 0 -3969 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1984.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '1984.5' to each side of the equation. -1984.5 + 5.5x + 1984.5 + x2 = 0 + 1984.5 Reorder the terms: -1984.5 + 1984.5 + 5.5x + x2 = 0 + 1984.5 Combine like terms: -1984.5 + 1984.5 = 0.0 0.0 + 5.5x + x2 = 0 + 1984.5 5.5x + x2 = 0 + 1984.5 Combine like terms: 0 + 1984.5 = 1984.5 5.5x + x2 = 1984.5 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 = 1984.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 1984.5 + 7.5625 Combine like terms: 1984.5 + 7.5625 = 1992.0625 7.5625 + 5.5x + x2 = 1992.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 1992.0625 Calculate the square root of the right side: 44.632527376 Break this problem into two subproblems by setting (x + 2.75) equal to 44.632527376 and -44.632527376.Subproblem 1
x + 2.75 = 44.632527376 Simplifying x + 2.75 = 44.632527376 Reorder the terms: 2.75 + x = 44.632527376 Solving 2.75 + x = 44.632527376 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 = 44.632527376 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 44.632527376 + -2.75 x = 44.632527376 + -2.75 Combine like terms: 44.632527376 + -2.75 = 41.882527376 x = 41.882527376 Simplifying x = 41.882527376Subproblem 2
x + 2.75 = -44.632527376 Simplifying x + 2.75 = -44.632527376 Reorder the terms: 2.75 + x = -44.632527376 Solving 2.75 + x = -44.632527376 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 = -44.632527376 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -44.632527376 + -2.75 x = -44.632527376 + -2.75 Combine like terms: -44.632527376 + -2.75 = -47.382527376 x = -47.382527376 Simplifying x = -47.382527376Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.882527376, -47.382527376}
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