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Simplifying a2 + 5a = 4 Reorder the terms: 5a + a2 = 4 Solving 5a + a2 = 4 Solving for variable 'a'. Reorder the terms: -4 + 5a + a2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + 5a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5a + a2 = 0 + 4 5a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 5a + a2 = 4 The a term is 5a. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5a + 6.25 + a2 = 4 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5a + a2 = 10.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (a + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
a + 2.5 = 3.201562119 Simplifying a + 2.5 = 3.201562119 Reorder the terms: 2.5 + a = 3.201562119 Solving 2.5 + a = 3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 3.201562119 + -2.5 a = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 a = 0.701562119 Simplifying a = 0.701562119Subproblem 2
a + 2.5 = -3.201562119 Simplifying a + 2.5 = -3.201562119 Reorder the terms: 2.5 + a = -3.201562119 Solving 2.5 + a = -3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -3.201562119 + -2.5 a = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 a = -5.701562119 Simplifying a = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.701562119, -5.701562119}
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