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Simplifying 15a2 + -8 = 29a + 9 Reorder the terms: -8 + 15a2 = 29a + 9 Reorder the terms: -8 + 15a2 = 9 + 29a Solving -8 + 15a2 = 9 + 29a Solving for variable 'a'. Reorder the terms: -8 + -9 + -29a + 15a2 = 9 + 29a + -9 + -29a Combine like terms: -8 + -9 = -17 -17 + -29a + 15a2 = 9 + 29a + -9 + -29a Reorder the terms: -17 + -29a + 15a2 = 9 + -9 + 29a + -29a Combine like terms: 9 + -9 = 0 -17 + -29a + 15a2 = 0 + 29a + -29a -17 + -29a + 15a2 = 29a + -29a Combine like terms: 29a + -29a = 0 -17 + -29a + 15a2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.133333333 + -1.933333333a + a2 = 0 Move the constant term to the right: Add '1.133333333' to each side of the equation. -1.133333333 + -1.933333333a + 1.133333333 + a2 = 0 + 1.133333333 Reorder the terms: -1.133333333 + 1.133333333 + -1.933333333a + a2 = 0 + 1.133333333 Combine like terms: -1.133333333 + 1.133333333 = 0.000000000 0.000000000 + -1.933333333a + a2 = 0 + 1.133333333 -1.933333333a + a2 = 0 + 1.133333333 Combine like terms: 0 + 1.133333333 = 1.133333333 -1.933333333a + a2 = 1.133333333 The a term is -1.933333333a. Take half its coefficient (-0.9666666665). Square it (0.9344444441) and add it to both sides. Add '0.9344444441' to each side of the equation. -1.933333333a + 0.9344444441 + a2 = 1.133333333 + 0.9344444441 Reorder the terms: 0.9344444441 + -1.933333333a + a2 = 1.133333333 + 0.9344444441 Combine like terms: 1.133333333 + 0.9344444441 = 2.0677777771 0.9344444441 + -1.933333333a + a2 = 2.0677777771 Factor a perfect square on the left side: (a + -0.9666666665)(a + -0.9666666665) = 2.0677777771 Calculate the square root of the right side: 1.437976974 Break this problem into two subproblems by setting (a + -0.9666666665) equal to 1.437976974 and -1.437976974.Subproblem 1
a + -0.9666666665 = 1.437976974 Simplifying a + -0.9666666665 = 1.437976974 Reorder the terms: -0.9666666665 + a = 1.437976974 Solving -0.9666666665 + a = 1.437976974 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.9666666665' to each side of the equation. -0.9666666665 + 0.9666666665 + a = 1.437976974 + 0.9666666665 Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000 0.0000000000 + a = 1.437976974 + 0.9666666665 a = 1.437976974 + 0.9666666665 Combine like terms: 1.437976974 + 0.9666666665 = 2.4046436405 a = 2.4046436405 Simplifying a = 2.4046436405Subproblem 2
a + -0.9666666665 = -1.437976974 Simplifying a + -0.9666666665 = -1.437976974 Reorder the terms: -0.9666666665 + a = -1.437976974 Solving -0.9666666665 + a = -1.437976974 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.9666666665' to each side of the equation. -0.9666666665 + 0.9666666665 + a = -1.437976974 + 0.9666666665 Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000 0.0000000000 + a = -1.437976974 + 0.9666666665 a = -1.437976974 + 0.9666666665 Combine like terms: -1.437976974 + 0.9666666665 = -0.4713103075 a = -0.4713103075 Simplifying a = -0.4713103075Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.4046436405, -0.4713103075}
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