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Simplifying 3x(x + 22) = 41 Reorder the terms: 3x(22 + x) = 41 (22 * 3x + x * 3x) = 41 (66x + 3x2) = 41 Solving 66x + 3x2 = 41 Solving for variable 'x'. Reorder the terms: -41 + 66x + 3x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + 66x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.66666667 + 22x + x2 = 0 Move the constant term to the right: Add '13.66666667' to each side of the equation. -13.66666667 + 22x + 13.66666667 + x2 = 0 + 13.66666667 Reorder the terms: -13.66666667 + 13.66666667 + 22x + x2 = 0 + 13.66666667 Combine like terms: -13.66666667 + 13.66666667 = 0.00000000 0.00000000 + 22x + x2 = 0 + 13.66666667 22x + x2 = 0 + 13.66666667 Combine like terms: 0 + 13.66666667 = 13.66666667 22x + x2 = 13.66666667 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 13.66666667 + 121 Reorder the terms: 121 + 22x + x2 = 13.66666667 + 121 Combine like terms: 13.66666667 + 121 = 134.66666667 121 + 22x + x2 = 134.66666667 Factor a perfect square on the left side: (x + 11)(x + 11) = 134.66666667 Calculate the square root of the right side: 11.60459679 Break this problem into two subproblems by setting (x + 11) equal to 11.60459679 and -11.60459679.Subproblem 1
x + 11 = 11.60459679 Simplifying x + 11 = 11.60459679 Reorder the terms: 11 + x = 11.60459679 Solving 11 + x = 11.60459679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 11.60459679 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.60459679 + -11 x = 11.60459679 + -11 Combine like terms: 11.60459679 + -11 = 0.60459679 x = 0.60459679 Simplifying x = 0.60459679Subproblem 2
x + 11 = -11.60459679 Simplifying x + 11 = -11.60459679 Reorder the terms: 11 + x = -11.60459679 Solving 11 + x = -11.60459679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -11.60459679 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.60459679 + -11 x = -11.60459679 + -11 Combine like terms: -11.60459679 + -11 = -22.60459679 x = -22.60459679 Simplifying x = -22.60459679Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.60459679, -22.60459679}
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