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Simplifying a2 + -49a + 64 = 0 Reorder the terms: 64 + -49a + a2 = 0 Solving 64 + -49a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -49a + -64 + a2 = 0 + -64 Reorder the terms: 64 + -64 + -49a + a2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -49a + a2 = 0 + -64 -49a + a2 = 0 + -64 Combine like terms: 0 + -64 = -64 -49a + a2 = -64 The a term is -49a. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49a + 600.25 + a2 = -64 + 600.25 Reorder the terms: 600.25 + -49a + a2 = -64 + 600.25 Combine like terms: -64 + 600.25 = 536.25 600.25 + -49a + a2 = 536.25 Factor a perfect square on the left side: (a + -24.5)(a + -24.5) = 536.25 Calculate the square root of the right side: 23.157072354 Break this problem into two subproblems by setting (a + -24.5) equal to 23.157072354 and -23.157072354.Subproblem 1
a + -24.5 = 23.157072354 Simplifying a + -24.5 = 23.157072354 Reorder the terms: -24.5 + a = 23.157072354 Solving -24.5 + a = 23.157072354 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + a = 23.157072354 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + a = 23.157072354 + 24.5 a = 23.157072354 + 24.5 Combine like terms: 23.157072354 + 24.5 = 47.657072354 a = 47.657072354 Simplifying a = 47.657072354Subproblem 2
a + -24.5 = -23.157072354 Simplifying a + -24.5 = -23.157072354 Reorder the terms: -24.5 + a = -23.157072354 Solving -24.5 + a = -23.157072354 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + a = -23.157072354 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + a = -23.157072354 + 24.5 a = -23.157072354 + 24.5 Combine like terms: -23.157072354 + 24.5 = 1.342927646 a = 1.342927646 Simplifying a = 1.342927646Solution
The solution to the problem is based on the solutions from the subproblems. a = {47.657072354, 1.342927646}
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