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Simplifying 0 = 60 + -32x + 3x2 Solving 0 = 60 + -32x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + 32x + -3x2 = 60 + -32x + 3x2 + -60 + 32x + -3x2 Reorder the terms: -60 + 32x + -3x2 = 60 + -60 + -32x + 32x + 3x2 + -3x2 Combine like terms: 60 + -60 = 0 -60 + 32x + -3x2 = 0 + -32x + 32x + 3x2 + -3x2 -60 + 32x + -3x2 = -32x + 32x + 3x2 + -3x2 Combine like terms: -32x + 32x = 0 -60 + 32x + -3x2 = 0 + 3x2 + -3x2 -60 + 32x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -60 + 32x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 20 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -10.66666667x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -10.66666667x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -10.66666667x + x2 = 0 + -20 -10.66666667x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -10.66666667x + x2 = -20 The x term is -10.66666667x. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667x + 28.44444446 + x2 = -20 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = -20 + 28.44444446 Combine like terms: -20 + 28.44444446 = 8.44444446 28.44444446 + -10.66666667x + x2 = 8.44444446 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 8.44444446 Calculate the square root of the right side: 2.905932632 Break this problem into two subproblems by setting (x + -5.333333335) equal to 2.905932632 and -2.905932632.Subproblem 1
x + -5.333333335 = 2.905932632 Simplifying x + -5.333333335 = 2.905932632 Reorder the terms: -5.333333335 + x = 2.905932632 Solving -5.333333335 + x = 2.905932632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = 2.905932632 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 2.905932632 + 5.333333335 x = 2.905932632 + 5.333333335 Combine like terms: 2.905932632 + 5.333333335 = 8.239265967 x = 8.239265967 Simplifying x = 8.239265967Subproblem 2
x + -5.333333335 = -2.905932632 Simplifying x + -5.333333335 = -2.905932632 Reorder the terms: -5.333333335 + x = -2.905932632 Solving -5.333333335 + x = -2.905932632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = -2.905932632 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -2.905932632 + 5.333333335 x = -2.905932632 + 5.333333335 Combine like terms: -2.905932632 + 5.333333335 = 2.427400703 x = 2.427400703 Simplifying x = 2.427400703Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.239265967, 2.427400703}
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