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Simplifying 9a2 + -22 = 8a Reorder the terms: -22 + 9a2 = 8a Solving -22 + 9a2 = 8a Solving for variable 'a'. Reorder the terms: -22 + -8a + 9a2 = 8a + -8a Combine like terms: 8a + -8a = 0 -22 + -8a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.444444444 + -0.8888888889a + a2 = 0 Move the constant term to the right: Add '2.444444444' to each side of the equation. -2.444444444 + -0.8888888889a + 2.444444444 + a2 = 0 + 2.444444444 Reorder the terms: -2.444444444 + 2.444444444 + -0.8888888889a + a2 = 0 + 2.444444444 Combine like terms: -2.444444444 + 2.444444444 = 0.000000000 0.000000000 + -0.8888888889a + a2 = 0 + 2.444444444 -0.8888888889a + a2 = 0 + 2.444444444 Combine like terms: 0 + 2.444444444 = 2.444444444 -0.8888888889a + a2 = 2.444444444 The a term is -0.8888888889a. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889a + 0.1975308642 + a2 = 2.444444444 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889a + a2 = 2.444444444 + 0.1975308642 Combine like terms: 2.444444444 + 0.1975308642 = 2.6419753082 0.1975308642 + -0.8888888889a + a2 = 2.6419753082 Factor a perfect square on the left side: (a + -0.4444444445)(a + -0.4444444445) = 2.6419753082 Calculate the square root of the right side: 1.625415426 Break this problem into two subproblems by setting (a + -0.4444444445) equal to 1.625415426 and -1.625415426.Subproblem 1
a + -0.4444444445 = 1.625415426 Simplifying a + -0.4444444445 = 1.625415426 Reorder the terms: -0.4444444445 + a = 1.625415426 Solving -0.4444444445 + a = 1.625415426 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + a = 1.625415426 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + a = 1.625415426 + 0.4444444445 a = 1.625415426 + 0.4444444445 Combine like terms: 1.625415426 + 0.4444444445 = 2.0698598705 a = 2.0698598705 Simplifying a = 2.0698598705Subproblem 2
a + -0.4444444445 = -1.625415426 Simplifying a + -0.4444444445 = -1.625415426 Reorder the terms: -0.4444444445 + a = -1.625415426 Solving -0.4444444445 + a = -1.625415426 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + a = -1.625415426 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + a = -1.625415426 + 0.4444444445 a = -1.625415426 + 0.4444444445 Combine like terms: -1.625415426 + 0.4444444445 = -1.1809709815 a = -1.1809709815 Simplifying a = -1.1809709815Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.0698598705, -1.1809709815}
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