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Simplifying a2 + -28a + -28 = 0 Reorder the terms: -28 + -28a + a2 = 0 Solving -28 + -28a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -28a + 28 + a2 = 0 + 28 Reorder the terms: -28 + 28 + -28a + a2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -28a + a2 = 0 + 28 -28a + a2 = 0 + 28 Combine like terms: 0 + 28 = 28 -28a + a2 = 28 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 = 28 + 196 Reorder the terms: 196 + -28a + a2 = 28 + 196 Combine like terms: 28 + 196 = 224 196 + -28a + a2 = 224 Factor a perfect square on the left side: (a + -14)(a + -14) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (a + -14) equal to 14.966629547 and -14.966629547.Subproblem 1
a + -14 = 14.966629547 Simplifying a + -14 = 14.966629547 Reorder the terms: -14 + a = 14.966629547 Solving -14 + a = 14.966629547 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 = 14.966629547 + 14 Combine like terms: -14 + 14 = 0 0 + a = 14.966629547 + 14 a = 14.966629547 + 14 Combine like terms: 14.966629547 + 14 = 28.966629547 a = 28.966629547 Simplifying a = 28.966629547Subproblem 2
a + -14 = -14.966629547 Simplifying a + -14 = -14.966629547 Reorder the terms: -14 + a = -14.966629547 Solving -14 + a = -14.966629547 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 = -14.966629547 + 14 Combine like terms: -14 + 14 = 0 0 + a = -14.966629547 + 14 a = -14.966629547 + 14 Combine like terms: -14.966629547 + 14 = -0.966629547 a = -0.966629547 Simplifying a = -0.966629547Solution
The solution to the problem is based on the solutions from the subproblems. a = {28.966629547, -0.966629547}
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