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Simplifying a2 + -5.5a + 7.5 = 0 Reorder the terms: 7.5 + -5.5a + a2 = 0 Solving 7.5 + -5.5a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -5.5a + -7.5 + a2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -5.5a + a2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -5.5a + a2 = 0 + -7.5 -5.5a + a2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -5.5a + a2 = -7.5 The a term is -5.5a. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5a + 7.5625 + a2 = -7.5 + 7.5625 Reorder the terms: 7.5625 + -5.5a + a2 = -7.5 + 7.5625 Combine like terms: -7.5 + 7.5625 = 0.0625 7.5625 + -5.5a + a2 = 0.0625 Factor a perfect square on the left side: (a + -2.75)(a + -2.75) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (a + -2.75) equal to 0.25 and -0.25.Subproblem 1
a + -2.75 = 0.25 Simplifying a + -2.75 = 0.25 Reorder the terms: -2.75 + a = 0.25 Solving -2.75 + a = 0.25 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = 0.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = 0.25 + 2.75 a = 0.25 + 2.75 Combine like terms: 0.25 + 2.75 = 3 a = 3 Simplifying a = 3Subproblem 2
a + -2.75 = -0.25 Simplifying a + -2.75 = -0.25 Reorder the terms: -2.75 + a = -0.25 Solving -2.75 + a = -0.25 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = -0.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = -0.25 + 2.75 a = -0.25 + 2.75 Combine like terms: -0.25 + 2.75 = 2.5 a = 2.5 Simplifying a = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. a = {3, 2.5}
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