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Simplifying 9x2 + -96x + 172 = 0 Reorder the terms: 172 + -96x + 9x2 = 0 Solving 172 + -96x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 19.11111111 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '-19.11111111' to each side of the equation. 19.11111111 + -10.66666667x + -19.11111111 + x2 = 0 + -19.11111111 Reorder the terms: 19.11111111 + -19.11111111 + -10.66666667x + x2 = 0 + -19.11111111 Combine like terms: 19.11111111 + -19.11111111 = 0.00000000 0.00000000 + -10.66666667x + x2 = 0 + -19.11111111 -10.66666667x + x2 = 0 + -19.11111111 Combine like terms: 0 + -19.11111111 = -19.11111111 -10.66666667x + x2 = -19.11111111 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 = -19.11111111 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = -19.11111111 + 28.44444446 Combine like terms: -19.11111111 + 28.44444446 = 9.33333335 28.44444446 + -10.66666667x + x2 = 9.33333335 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 9.33333335 Calculate the square root of the right side: 3.055050466 Break this problem into two subproblems by setting (x + -5.333333335) equal to 3.055050466 and -3.055050466.Subproblem 1
x + -5.333333335 = 3.055050466 Simplifying x + -5.333333335 = 3.055050466 Reorder the terms: -5.333333335 + x = 3.055050466 Solving -5.333333335 + x = 3.055050466 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 = 3.055050466 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 3.055050466 + 5.333333335 x = 3.055050466 + 5.333333335 Combine like terms: 3.055050466 + 5.333333335 = 8.388383801 x = 8.388383801 Simplifying x = 8.388383801Subproblem 2
x + -5.333333335 = -3.055050466 Simplifying x + -5.333333335 = -3.055050466 Reorder the terms: -5.333333335 + x = -3.055050466 Solving -5.333333335 + x = -3.055050466 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 = -3.055050466 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -3.055050466 + 5.333333335 x = -3.055050466 + 5.333333335 Combine like terms: -3.055050466 + 5.333333335 = 2.278282869 x = 2.278282869 Simplifying x = 2.278282869Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.388383801, 2.278282869}
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