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Simplifying 3x2 + 32x + -64 = 0 Reorder the terms: -64 + 32x + 3x2 = 0 Solving -64 + 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'. -21.33333333 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + 10.66666667x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + 10.66666667x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + 10.66666667x + x2 = 0 + 21.33333333 10.66666667x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 10.66666667x + x2 = 21.33333333 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 = 21.33333333 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = 21.33333333 + 28.44444446 Combine like terms: 21.33333333 + 28.44444446 = 49.77777779 28.44444446 + 10.66666667x + x2 = 49.77777779 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 49.77777779 Calculate the square root of the right side: 7.05533683 Break this problem into two subproblems by setting (x + 5.333333335) equal to 7.05533683 and -7.05533683.Subproblem 1
x + 5.333333335 = 7.05533683 Simplifying x + 5.333333335 = 7.05533683 Reorder the terms: 5.333333335 + x = 7.05533683 Solving 5.333333335 + x = 7.05533683 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 = 7.05533683 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 7.05533683 + -5.333333335 x = 7.05533683 + -5.333333335 Combine like terms: 7.05533683 + -5.333333335 = 1.722003495 x = 1.722003495 Simplifying x = 1.722003495Subproblem 2
x + 5.333333335 = -7.05533683 Simplifying x + 5.333333335 = -7.05533683 Reorder the terms: 5.333333335 + x = -7.05533683 Solving 5.333333335 + x = -7.05533683 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 = -7.05533683 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -7.05533683 + -5.333333335 x = -7.05533683 + -5.333333335 Combine like terms: -7.05533683 + -5.333333335 = -12.388670165 x = -12.388670165 Simplifying x = -12.388670165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.722003495, -12.388670165}
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