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Simplifying a2 = 9 + -5a Solving a2 = 9 + -5a Solving for variable 'a'. Reorder the terms: -9 + 5a + a2 = 9 + -5a + -9 + 5a Reorder the terms: -9 + 5a + a2 = 9 + -9 + -5a + 5a Combine like terms: 9 + -9 = 0 -9 + 5a + a2 = 0 + -5a + 5a -9 + 5a + a2 = -5a + 5a Combine like terms: -5a + 5a = 0 -9 + 5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 5a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + 5a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5a + a2 = 0 + 9 5a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 5a + a2 = 9 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 = 9 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + 5a + a2 = 15.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (a + 2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
a + 2.5 = 3.905124838 Simplifying a + 2.5 = 3.905124838 Reorder the terms: 2.5 + a = 3.905124838 Solving 2.5 + a = 3.905124838 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 = 3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 3.905124838 + -2.5 a = 3.905124838 + -2.5 Combine like terms: 3.905124838 + -2.5 = 1.405124838 a = 1.405124838 Simplifying a = 1.405124838Subproblem 2
a + 2.5 = -3.905124838 Simplifying a + 2.5 = -3.905124838 Reorder the terms: 2.5 + a = -3.905124838 Solving 2.5 + a = -3.905124838 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 = -3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -3.905124838 + -2.5 a = -3.905124838 + -2.5 Combine like terms: -3.905124838 + -2.5 = -6.405124838 a = -6.405124838 Simplifying a = -6.405124838Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.405124838, -6.405124838}
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