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Simplifying 3(a2 + 2a) = 2a2 + 9 Reorder the terms: 3(2a + a2) = 2a2 + 9 (2a * 3 + a2 * 3) = 2a2 + 9 (6a + 3a2) = 2a2 + 9 Reorder the terms: 6a + 3a2 = 9 + 2a2 Solving 6a + 3a2 = 9 + 2a2 Solving for variable 'a'. Reorder the terms: -9 + 6a + 3a2 + -2a2 = 9 + 2a2 + -9 + -2a2 Combine like terms: 3a2 + -2a2 = 1a2 -9 + 6a + 1a2 = 9 + 2a2 + -9 + -2a2 Reorder the terms: -9 + 6a + 1a2 = 9 + -9 + 2a2 + -2a2 Combine like terms: 9 + -9 = 0 -9 + 6a + 1a2 = 0 + 2a2 + -2a2 -9 + 6a + 1a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 -9 + 6a + 1a2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 6a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + 6a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6a + a2 = 0 + 9 6a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 6a + a2 = 9 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 9 + 9 Reorder the terms: 9 + 6a + a2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6a + a2 = 18 Factor a perfect square on the left side: (a + 3)(a + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (a + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
a + 3 = 4.242640687 Simplifying a + 3 = 4.242640687 Reorder the terms: 3 + a = 4.242640687 Solving 3 + a = 4.242640687 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + a = 4.242640687 + -3 a = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 a = 1.242640687 Simplifying a = 1.242640687Subproblem 2
a + 3 = -4.242640687 Simplifying a + 3 = -4.242640687 Reorder the terms: 3 + a = -4.242640687 Solving 3 + a = -4.242640687 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + a = -4.242640687 + -3 a = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 a = -7.242640687 Simplifying a = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.242640687, -7.242640687}
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