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Simplifying a2 + -25a + 2 = 0 Reorder the terms: 2 + -25a + a2 = 0 Solving 2 + -25a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -25a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + -25a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -25a + a2 = 0 + -2 -25a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 -25a + a2 = -2 The a term is -25a. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25a + 156.25 + a2 = -2 + 156.25 Reorder the terms: 156.25 + -25a + a2 = -2 + 156.25 Combine like terms: -2 + 156.25 = 154.25 156.25 + -25a + a2 = 154.25 Factor a perfect square on the left side: (a + -12.5)(a + -12.5) = 154.25 Calculate the square root of the right side: 12.419742348 Break this problem into two subproblems by setting (a + -12.5) equal to 12.419742348 and -12.419742348.Subproblem 1
a + -12.5 = 12.419742348 Simplifying a + -12.5 = 12.419742348 Reorder the terms: -12.5 + a = 12.419742348 Solving -12.5 + a = 12.419742348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + a = 12.419742348 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = 12.419742348 + 12.5 a = 12.419742348 + 12.5 Combine like terms: 12.419742348 + 12.5 = 24.919742348 a = 24.919742348 Simplifying a = 24.919742348Subproblem 2
a + -12.5 = -12.419742348 Simplifying a + -12.5 = -12.419742348 Reorder the terms: -12.5 + a = -12.419742348 Solving -12.5 + a = -12.419742348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + a = -12.419742348 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = -12.419742348 + 12.5 a = -12.419742348 + 12.5 Combine like terms: -12.419742348 + 12.5 = 0.080257652 a = 0.080257652 Simplifying a = 0.080257652Solution
The solution to the problem is based on the solutions from the subproblems. a = {24.919742348, 0.080257652}
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