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Simplifying a2 + 4a + -360 = 0 Reorder the terms: -360 + 4a + a2 = 0 Solving -360 + 4a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 4a + 360 + a2 = 0 + 360 Reorder the terms: -360 + 360 + 4a + a2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 4a + a2 = 0 + 360 4a + a2 = 0 + 360 Combine like terms: 0 + 360 = 360 4a + a2 = 360 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 360 + 4 Reorder the terms: 4 + 4a + a2 = 360 + 4 Combine like terms: 360 + 4 = 364 4 + 4a + a2 = 364 Factor a perfect square on the left side: (a + 2)(a + 2) = 364 Calculate the square root of the right side: 19.078784028 Break this problem into two subproblems by setting (a + 2) equal to 19.078784028 and -19.078784028.Subproblem 1
a + 2 = 19.078784028 Simplifying a + 2 = 19.078784028 Reorder the terms: 2 + a = 19.078784028 Solving 2 + a = 19.078784028 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 19.078784028 + -2 Combine like terms: 2 + -2 = 0 0 + a = 19.078784028 + -2 a = 19.078784028 + -2 Combine like terms: 19.078784028 + -2 = 17.078784028 a = 17.078784028 Simplifying a = 17.078784028Subproblem 2
a + 2 = -19.078784028 Simplifying a + 2 = -19.078784028 Reorder the terms: 2 + a = -19.078784028 Solving 2 + a = -19.078784028 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -19.078784028 + -2 Combine like terms: 2 + -2 = 0 0 + a = -19.078784028 + -2 a = -19.078784028 + -2 Combine like terms: -19.078784028 + -2 = -21.078784028 a = -21.078784028 Simplifying a = -21.078784028Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.078784028, -21.078784028}
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