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Simplifying 9a2 + -64a + 36 = 0 Reorder the terms: 36 + -64a + 9a2 = 0 Solving 36 + -64a + 9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4 + -7.111111111a + a2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7.111111111a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -7.111111111a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7.111111111a + a2 = 0 + -4 -7.111111111a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7.111111111a + a2 = -4 The a term is -7.111111111a. Take half its coefficient (-3.555555556). Square it (12.64197531) and add it to both sides. Add '12.64197531' to each side of the equation. -7.111111111a + 12.64197531 + a2 = -4 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111a + a2 = -4 + 12.64197531 Combine like terms: -4 + 12.64197531 = 8.64197531 12.64197531 + -7.111111111a + a2 = 8.64197531 Factor a perfect square on the left side: (a + -3.555555556)(a + -3.555555556) = 8.64197531 Calculate the square root of the right side: 2.939723679 Break this problem into two subproblems by setting (a + -3.555555556) equal to 2.939723679 and -2.939723679.Subproblem 1
a + -3.555555556 = 2.939723679 Simplifying a + -3.555555556 = 2.939723679 Reorder the terms: -3.555555556 + a = 2.939723679 Solving -3.555555556 + a = 2.939723679 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + a = 2.939723679 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + a = 2.939723679 + 3.555555556 a = 2.939723679 + 3.555555556 Combine like terms: 2.939723679 + 3.555555556 = 6.495279235 a = 6.495279235 Simplifying a = 6.495279235Subproblem 2
a + -3.555555556 = -2.939723679 Simplifying a + -3.555555556 = -2.939723679 Reorder the terms: -3.555555556 + a = -2.939723679 Solving -3.555555556 + a = -2.939723679 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + a = -2.939723679 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + a = -2.939723679 + 3.555555556 a = -2.939723679 + 3.555555556 Combine like terms: -2.939723679 + 3.555555556 = 0.615831877 a = 0.615831877 Simplifying a = 0.615831877Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.495279235, 0.615831877}
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