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Simplifying 3x2 + -32x + 27 = 0 Reorder the terms: 27 + -32x + 3x2 = 0 Solving 27 + -32x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -10.66666667x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -10.66666667x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -10.66666667x + x2 = 0 + -9 -10.66666667x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -10.66666667x + x2 = -9 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 = -9 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = -9 + 28.44444446 Combine like terms: -9 + 28.44444446 = 19.44444446 28.44444446 + -10.66666667x + x2 = 19.44444446 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 19.44444446 Calculate the square root of the right side: 4.40958552 Break this problem into two subproblems by setting (x + -5.333333335) equal to 4.40958552 and -4.40958552.Subproblem 1
x + -5.333333335 = 4.40958552 Simplifying x + -5.333333335 = 4.40958552 Reorder the terms: -5.333333335 + x = 4.40958552 Solving -5.333333335 + x = 4.40958552 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 = 4.40958552 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 4.40958552 + 5.333333335 x = 4.40958552 + 5.333333335 Combine like terms: 4.40958552 + 5.333333335 = 9.742918855 x = 9.742918855 Simplifying x = 9.742918855Subproblem 2
x + -5.333333335 = -4.40958552 Simplifying x + -5.333333335 = -4.40958552 Reorder the terms: -5.333333335 + x = -4.40958552 Solving -5.333333335 + x = -4.40958552 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 = -4.40958552 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -4.40958552 + 5.333333335 x = -4.40958552 + 5.333333335 Combine like terms: -4.40958552 + 5.333333335 = 0.923747815 x = 0.923747815 Simplifying x = 0.923747815Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.742918855, 0.923747815}
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