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Simplifying a2 + -28a + 35 = 0 Reorder the terms: 35 + -28a + a2 = 0 Solving 35 + -28a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -28a + -35 + a2 = 0 + -35 Reorder the terms: 35 + -35 + -28a + a2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -28a + a2 = 0 + -35 -28a + a2 = 0 + -35 Combine like terms: 0 + -35 = -35 -28a + a2 = -35 The a term is -28a. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28a + 196 + a2 = -35 + 196 Reorder the terms: 196 + -28a + a2 = -35 + 196 Combine like terms: -35 + 196 = 161 196 + -28a + a2 = 161 Factor a perfect square on the left side: (a + -14)(a + -14) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (a + -14) equal to 12.68857754 and -12.68857754.Subproblem 1
a + -14 = 12.68857754 Simplifying a + -14 = 12.68857754 Reorder the terms: -14 + a = 12.68857754 Solving -14 + a = 12.68857754 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a = 12.68857754 + 14 Combine like terms: -14 + 14 = 0 0 + a = 12.68857754 + 14 a = 12.68857754 + 14 Combine like terms: 12.68857754 + 14 = 26.68857754 a = 26.68857754 Simplifying a = 26.68857754Subproblem 2
a + -14 = -12.68857754 Simplifying a + -14 = -12.68857754 Reorder the terms: -14 + a = -12.68857754 Solving -14 + a = -12.68857754 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a = -12.68857754 + 14 Combine like terms: -14 + 14 = 0 0 + a = -12.68857754 + 14 a = -12.68857754 + 14 Combine like terms: -12.68857754 + 14 = 1.31142246 a = 1.31142246 Simplifying a = 1.31142246Solution
The solution to the problem is based on the solutions from the subproblems. a = {26.68857754, 1.31142246}
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