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Simplifying a2 + 6a + -25 = 0 Reorder the terms: -25 + 6a + a2 = 0 Solving -25 + 6a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 6a + 25 + a2 = 0 + 25 Reorder the terms: -25 + 25 + 6a + a2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 6a + a2 = 0 + 25 6a + a2 = 0 + 25 Combine like terms: 0 + 25 = 25 6a + a2 = 25 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 = 25 + 9 Reorder the terms: 9 + 6a + a2 = 25 + 9 Combine like terms: 25 + 9 = 34 9 + 6a + a2 = 34 Factor a perfect square on the left side: (a + 3)(a + 3) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (a + 3) equal to 5.830951895 and -5.830951895.Subproblem 1
a + 3 = 5.830951895 Simplifying a + 3 = 5.830951895 Reorder the terms: 3 + a = 5.830951895 Solving 3 + a = 5.830951895 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 = 5.830951895 + -3 Combine like terms: 3 + -3 = 0 0 + a = 5.830951895 + -3 a = 5.830951895 + -3 Combine like terms: 5.830951895 + -3 = 2.830951895 a = 2.830951895 Simplifying a = 2.830951895Subproblem 2
a + 3 = -5.830951895 Simplifying a + 3 = -5.830951895 Reorder the terms: 3 + a = -5.830951895 Solving 3 + a = -5.830951895 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 = -5.830951895 + -3 Combine like terms: 3 + -3 = 0 0 + a = -5.830951895 + -3 a = -5.830951895 + -3 Combine like terms: -5.830951895 + -3 = -8.830951895 a = -8.830951895 Simplifying a = -8.830951895Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.830951895, -8.830951895}
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