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Simplifying (11 + 2x) * x = 63 * 2 Reorder the terms for easier multiplication: x(11 + 2x) = 63 * 2 (11 * x + 2x * x) = 63 * 2 (11x + 2x2) = 63 * 2 Multiply 63 * 2 11x + 2x2 = 126 Solving 11x + 2x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 11x + 2x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -63 + 5.5x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 5.5x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 5.5x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 5.5x + x2 = 0 + 63 5.5x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 5.5x + x2 = 63 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 = 63 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 63 + 7.5625 Combine like terms: 63 + 7.5625 = 70.5625 7.5625 + 5.5x + x2 = 70.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 70.5625 Calculate the square root of the right side: 8.400148808 Break this problem into two subproblems by setting (x + 2.75) equal to 8.400148808 and -8.400148808.Subproblem 1
x + 2.75 = 8.400148808 Simplifying x + 2.75 = 8.400148808 Reorder the terms: 2.75 + x = 8.400148808 Solving 2.75 + x = 8.400148808 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 = 8.400148808 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 8.400148808 + -2.75 x = 8.400148808 + -2.75 Combine like terms: 8.400148808 + -2.75 = 5.650148808 x = 5.650148808 Simplifying x = 5.650148808Subproblem 2
x + 2.75 = -8.400148808 Simplifying x + 2.75 = -8.400148808 Reorder the terms: 2.75 + x = -8.400148808 Solving 2.75 + x = -8.400148808 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 = -8.400148808 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -8.400148808 + -2.75 x = -8.400148808 + -2.75 Combine like terms: -8.400148808 + -2.75 = -11.150148808 x = -11.150148808 Simplifying x = -11.150148808Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.650148808, -11.150148808}
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