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Simplifying a2 + -5a = 10 Reorder the terms: -5a + a2 = 10 Solving -5a + a2 = 10 Solving for variable 'a'. Reorder the terms: -10 + -5a + a2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -5a + 10 + a2 = 0 + 10 Reorder the terms: -10 + 10 + -5a + a2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5a + a2 = 0 + 10 -5a + a2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5a + a2 = 10 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 = 10 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 10 + 6.25 Combine like terms: 10 + 6.25 = 16.25 6.25 + -5a + a2 = 16.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (a + -2.5) equal to 4.031128874 and -4.031128874.Subproblem 1
a + -2.5 = 4.031128874 Simplifying a + -2.5 = 4.031128874 Reorder the terms: -2.5 + a = 4.031128874 Solving -2.5 + a = 4.031128874 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 = 4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 4.031128874 + 2.5 a = 4.031128874 + 2.5 Combine like terms: 4.031128874 + 2.5 = 6.531128874 a = 6.531128874 Simplifying a = 6.531128874Subproblem 2
a + -2.5 = -4.031128874 Simplifying a + -2.5 = -4.031128874 Reorder the terms: -2.5 + a = -4.031128874 Solving -2.5 + a = -4.031128874 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 = -4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -4.031128874 + 2.5 a = -4.031128874 + 2.5 Combine like terms: -4.031128874 + 2.5 = -1.531128874 a = -1.531128874 Simplifying a = -1.531128874Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.531128874, -1.531128874}
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