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Simplifying 9a2 + -17a + -21 = 8a2 + a Reorder the terms: -21 + -17a + 9a2 = 8a2 + a Reorder the terms: -21 + -17a + 9a2 = a + 8a2 Solving -21 + -17a + 9a2 = a + 8a2 Solving for variable 'a'. Reorder the terms: -21 + -17a + -1a + 9a2 + -8a2 = a + 8a2 + -1a + -8a2 Combine like terms: -17a + -1a = -18a -21 + -18a + 9a2 + -8a2 = a + 8a2 + -1a + -8a2 Combine like terms: 9a2 + -8a2 = 1a2 -21 + -18a + 1a2 = a + 8a2 + -1a + -8a2 Reorder the terms: -21 + -18a + 1a2 = a + -1a + 8a2 + -8a2 Combine like terms: a + -1a = 0 -21 + -18a + 1a2 = 0 + 8a2 + -8a2 -21 + -18a + 1a2 = 8a2 + -8a2 Combine like terms: 8a2 + -8a2 = 0 -21 + -18a + 1a2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -18a + 21 + a2 = 0 + 21 Reorder the terms: -21 + 21 + -18a + a2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -18a + a2 = 0 + 21 -18a + a2 = 0 + 21 Combine like terms: 0 + 21 = 21 -18a + a2 = 21 The a term is -18a. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18a + 81 + a2 = 21 + 81 Reorder the terms: 81 + -18a + a2 = 21 + 81 Combine like terms: 21 + 81 = 102 81 + -18a + a2 = 102 Factor a perfect square on the left side: (a + -9)(a + -9) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (a + -9) equal to 10.099504938 and -10.099504938.Subproblem 1
a + -9 = 10.099504938 Simplifying a + -9 = 10.099504938 Reorder the terms: -9 + a = 10.099504938 Solving -9 + a = 10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = 10.099504938 + 9 Combine like terms: -9 + 9 = 0 0 + a = 10.099504938 + 9 a = 10.099504938 + 9 Combine like terms: 10.099504938 + 9 = 19.099504938 a = 19.099504938 Simplifying a = 19.099504938Subproblem 2
a + -9 = -10.099504938 Simplifying a + -9 = -10.099504938 Reorder the terms: -9 + a = -10.099504938 Solving -9 + a = -10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = -10.099504938 + 9 Combine like terms: -9 + 9 = 0 0 + a = -10.099504938 + 9 a = -10.099504938 + 9 Combine like terms: -10.099504938 + 9 = -1.099504938 a = -1.099504938 Simplifying a = -1.099504938Solution
The solution to the problem is based on the solutions from the subproblems. a = {19.099504938, -1.099504938}
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