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Simplifying a2 + 6a = 2 Reorder the terms: 6a + a2 = 2 Solving 6a + a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + 6a + a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 6a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 6a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6a + a2 = 0 + 2 6a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 6a + a2 = 2 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 = 2 + 9 Reorder the terms: 9 + 6a + a2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6a + a2 = 11 Factor a perfect square on the left side: (a + 3)(a + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (a + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
a + 3 = 3.31662479 Simplifying a + 3 = 3.31662479 Reorder the terms: 3 + a = 3.31662479 Solving 3 + a = 3.31662479 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 = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.31662479 + -3 a = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 a = 0.31662479 Simplifying a = 0.31662479Subproblem 2
a + 3 = -3.31662479 Simplifying a + 3 = -3.31662479 Reorder the terms: 3 + a = -3.31662479 Solving 3 + a = -3.31662479 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 = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.31662479 + -3 a = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 a = -6.31662479 Simplifying a = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.31662479, -6.31662479}
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