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Simplifying (-3x + 60)(-3x + 60) + 2 = x Reorder the terms: (60 + -3x)(-3x + 60) + 2 = x Reorder the terms: (60 + -3x)(60 + -3x) + 2 = x Multiply (60 + -3x) * (60 + -3x) (60(60 + -3x) + -3x * (60 + -3x)) + 2 = x ((60 * 60 + -3x * 60) + -3x * (60 + -3x)) + 2 = x ((3600 + -180x) + -3x * (60 + -3x)) + 2 = x (3600 + -180x + (60 * -3x + -3x * -3x)) + 2 = x (3600 + -180x + (-180x + 9x2)) + 2 = x Combine like terms: -180x + -180x = -360x (3600 + -360x + 9x2) + 2 = x Reorder the terms: 3600 + 2 + -360x + 9x2 = x Combine like terms: 3600 + 2 = 3602 3602 + -360x + 9x2 = x Solving 3602 + -360x + 9x2 = x Solving for variable 'x'. Reorder the terms: 3602 + -360x + -1x + 9x2 = x + -1x Combine like terms: -360x + -1x = -361x 3602 + -361x + 9x2 = x + -1x Combine like terms: x + -1x = 0 3602 + -361x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 400.2222222 + -40.11111111x + x2 = 0 Move the constant term to the right: Add '-400.2222222' to each side of the equation. 400.2222222 + -40.11111111x + -400.2222222 + x2 = 0 + -400.2222222 Reorder the terms: 400.2222222 + -400.2222222 + -40.11111111x + x2 = 0 + -400.2222222 Combine like terms: 400.2222222 + -400.2222222 = 0.0000000 0.0000000 + -40.11111111x + x2 = 0 + -400.2222222 -40.11111111x + x2 = 0 + -400.2222222 Combine like terms: 0 + -400.2222222 = -400.2222222 -40.11111111x + x2 = -400.2222222 The x term is -40.11111111x. Take half its coefficient (-20.05555556). Square it (402.2253088) and add it to both sides. Add '402.2253088' to each side of the equation. -40.11111111x + 402.2253088 + x2 = -400.2222222 + 402.2253088 Reorder the terms: 402.2253088 + -40.11111111x + x2 = -400.2222222 + 402.2253088 Combine like terms: -400.2222222 + 402.2253088 = 2.0030866 402.2253088 + -40.11111111x + x2 = 2.0030866 Factor a perfect square on the left side: (x + -20.05555556)(x + -20.05555556) = 2.0030866 Calculate the square root of the right side: 1.41530442 Break this problem into two subproblems by setting (x + -20.05555556) equal to 1.41530442 and -1.41530442.Subproblem 1
x + -20.05555556 = 1.41530442 Simplifying x + -20.05555556 = 1.41530442 Reorder the terms: -20.05555556 + x = 1.41530442 Solving -20.05555556 + x = 1.41530442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.05555556' to each side of the equation. -20.05555556 + 20.05555556 + x = 1.41530442 + 20.05555556 Combine like terms: -20.05555556 + 20.05555556 = 0.00000000 0.00000000 + x = 1.41530442 + 20.05555556 x = 1.41530442 + 20.05555556 Combine like terms: 1.41530442 + 20.05555556 = 21.47085998 x = 21.47085998 Simplifying x = 21.47085998Subproblem 2
x + -20.05555556 = -1.41530442 Simplifying x + -20.05555556 = -1.41530442 Reorder the terms: -20.05555556 + x = -1.41530442 Solving -20.05555556 + x = -1.41530442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.05555556' to each side of the equation. -20.05555556 + 20.05555556 + x = -1.41530442 + 20.05555556 Combine like terms: -20.05555556 + 20.05555556 = 0.00000000 0.00000000 + x = -1.41530442 + 20.05555556 x = -1.41530442 + 20.05555556 Combine like terms: -1.41530442 + 20.05555556 = 18.64025114 x = 18.64025114 Simplifying x = 18.64025114Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.47085998, 18.64025114}
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