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Simplifying a(a + 4) = 44 Reorder the terms: a(4 + a) = 44 (4 * a + a * a) = 44 (4a + a2) = 44 Solving 4a + a2 = 44 Solving for variable 'a'. Reorder the terms: -44 + 4a + a2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 4a + 44 + a2 = 0 + 44 Reorder the terms: -44 + 44 + 4a + a2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 4a + a2 = 0 + 44 4a + a2 = 0 + 44 Combine like terms: 0 + 44 = 44 4a + a2 = 44 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 = 44 + 4 Reorder the terms: 4 + 4a + a2 = 44 + 4 Combine like terms: 44 + 4 = 48 4 + 4a + a2 = 48 Factor a perfect square on the left side: (a + 2)(a + 2) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (a + 2) equal to 6.92820323 and -6.92820323.Subproblem 1
a + 2 = 6.92820323 Simplifying a + 2 = 6.92820323 Reorder the terms: 2 + a = 6.92820323 Solving 2 + a = 6.92820323 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 = 6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + a = 6.92820323 + -2 a = 6.92820323 + -2 Combine like terms: 6.92820323 + -2 = 4.92820323 a = 4.92820323 Simplifying a = 4.92820323Subproblem 2
a + 2 = -6.92820323 Simplifying a + 2 = -6.92820323 Reorder the terms: 2 + a = -6.92820323 Solving 2 + a = -6.92820323 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 = -6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + a = -6.92820323 + -2 a = -6.92820323 + -2 Combine like terms: -6.92820323 + -2 = -8.92820323 a = -8.92820323 Simplifying a = -8.92820323Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.92820323, -8.92820323}
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