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Simplifying 9a2 + -21 = 13a Reorder the terms: -21 + 9a2 = 13a Solving -21 + 9a2 = 13a Solving for variable 'a'. Reorder the terms: -21 + -13a + 9a2 = 13a + -13a Combine like terms: 13a + -13a = 0 -21 + -13a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.333333333 + -1.444444444a + a2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -1.444444444a + 2.333333333 + a2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -1.444444444a + a2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -1.444444444a + a2 = 0 + 2.333333333 -1.444444444a + a2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -1.444444444a + a2 = 2.333333333 The a term is -1.444444444a. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444a + 0.5216049380 + a2 = 2.333333333 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444a + a2 = 2.333333333 + 0.5216049380 Combine like terms: 2.333333333 + 0.5216049380 = 2.854938271 0.5216049380 + -1.444444444a + a2 = 2.854938271 Factor a perfect square on the left side: (a + -0.722222222)(a + -0.722222222) = 2.854938271 Calculate the square root of the right side: 1.689656258 Break this problem into two subproblems by setting (a + -0.722222222) equal to 1.689656258 and -1.689656258.Subproblem 1
a + -0.722222222 = 1.689656258 Simplifying a + -0.722222222 = 1.689656258 Reorder the terms: -0.722222222 + a = 1.689656258 Solving -0.722222222 + a = 1.689656258 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + a = 1.689656258 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + a = 1.689656258 + 0.722222222 a = 1.689656258 + 0.722222222 Combine like terms: 1.689656258 + 0.722222222 = 2.41187848 a = 2.41187848 Simplifying a = 2.41187848Subproblem 2
a + -0.722222222 = -1.689656258 Simplifying a + -0.722222222 = -1.689656258 Reorder the terms: -0.722222222 + a = -1.689656258 Solving -0.722222222 + a = -1.689656258 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + a = -1.689656258 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + a = -1.689656258 + 0.722222222 a = -1.689656258 + 0.722222222 Combine like terms: -1.689656258 + 0.722222222 = -0.967434036 a = -0.967434036 Simplifying a = -0.967434036Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.41187848, -0.967434036}
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