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Simplifying 3x2 + 66x = -2 Reorder the terms: 66x + 3x2 = -2 Solving 66x + 3x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 66x + 3x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 66x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 22x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 22x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 22x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 22x + x2 = 0 + -0.6666666667 22x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 22x + x2 = -0.6666666667 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 = -0.6666666667 + 121 Reorder the terms: 121 + 22x + x2 = -0.6666666667 + 121 Combine like terms: -0.6666666667 + 121 = 120.3333333333 121 + 22x + x2 = 120.3333333333 Factor a perfect square on the left side: (x + 11)(x + 11) = 120.3333333333 Calculate the square root of the right side: 10.969655115 Break this problem into two subproblems by setting (x + 11) equal to 10.969655115 and -10.969655115.Subproblem 1
x + 11 = 10.969655115 Simplifying x + 11 = 10.969655115 Reorder the terms: 11 + x = 10.969655115 Solving 11 + x = 10.969655115 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 = 10.969655115 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.969655115 + -11 x = 10.969655115 + -11 Combine like terms: 10.969655115 + -11 = -0.030344885 x = -0.030344885 Simplifying x = -0.030344885Subproblem 2
x + 11 = -10.969655115 Simplifying x + 11 = -10.969655115 Reorder the terms: 11 + x = -10.969655115 Solving 11 + x = -10.969655115 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 = -10.969655115 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.969655115 + -11 x = -10.969655115 + -11 Combine like terms: -10.969655115 + -11 = -21.969655115 x = -21.969655115 Simplifying x = -21.969655115Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.030344885, -21.969655115}
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