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Simplifying 9x2 + -128x + 64 = 0 Reorder the terms: 64 + -128x + 9x2 = 0 Solving 64 + -128x + 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'. 7.111111111 + -14.22222222x + x2 = 0 Move the constant term to the right: Add '-7.111111111' to each side of the equation. 7.111111111 + -14.22222222x + -7.111111111 + x2 = 0 + -7.111111111 Reorder the terms: 7.111111111 + -7.111111111 + -14.22222222x + x2 = 0 + -7.111111111 Combine like terms: 7.111111111 + -7.111111111 = 0.000000000 0.000000000 + -14.22222222x + x2 = 0 + -7.111111111 -14.22222222x + x2 = 0 + -7.111111111 Combine like terms: 0 + -7.111111111 = -7.111111111 -14.22222222x + x2 = -7.111111111 The x term is -14.22222222x. Take half its coefficient (-7.11111111). Square it (50.56790122) and add it to both sides. Add '50.56790122' to each side of the equation. -14.22222222x + 50.56790122 + x2 = -7.111111111 + 50.56790122 Reorder the terms: 50.56790122 + -14.22222222x + x2 = -7.111111111 + 50.56790122 Combine like terms: -7.111111111 + 50.56790122 = 43.456790109 50.56790122 + -14.22222222x + x2 = 43.456790109 Factor a perfect square on the left side: (x + -7.11111111)(x + -7.11111111) = 43.456790109 Calculate the square root of the right side: 6.592176432 Break this problem into two subproblems by setting (x + -7.11111111) equal to 6.592176432 and -6.592176432.Subproblem 1
x + -7.11111111 = 6.592176432 Simplifying x + -7.11111111 = 6.592176432 Reorder the terms: -7.11111111 + x = 6.592176432 Solving -7.11111111 + x = 6.592176432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.11111111' to each side of the equation. -7.11111111 + 7.11111111 + x = 6.592176432 + 7.11111111 Combine like terms: -7.11111111 + 7.11111111 = 0.00000000 0.00000000 + x = 6.592176432 + 7.11111111 x = 6.592176432 + 7.11111111 Combine like terms: 6.592176432 + 7.11111111 = 13.703287542 x = 13.703287542 Simplifying x = 13.703287542Subproblem 2
x + -7.11111111 = -6.592176432 Simplifying x + -7.11111111 = -6.592176432 Reorder the terms: -7.11111111 + x = -6.592176432 Solving -7.11111111 + x = -6.592176432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.11111111' to each side of the equation. -7.11111111 + 7.11111111 + x = -6.592176432 + 7.11111111 Combine like terms: -7.11111111 + 7.11111111 = 0.00000000 0.00000000 + x = -6.592176432 + 7.11111111 x = -6.592176432 + 7.11111111 Combine like terms: -6.592176432 + 7.11111111 = 0.518934678 x = 0.518934678 Simplifying x = 0.518934678Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.703287542, 0.518934678}
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