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Simplifying a2 + -20a + 52 = 8 Reorder the terms: 52 + -20a + a2 = 8 Solving 52 + -20a + a2 = 8 Solving for variable 'a'. Reorder the terms: 52 + -8 + -20a + a2 = 8 + -8 Combine like terms: 52 + -8 = 44 44 + -20a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 44 + -20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + -20a + -44 + a2 = 0 + -44 Reorder the terms: 44 + -44 + -20a + a2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -20a + a2 = 0 + -44 -20a + a2 = 0 + -44 Combine like terms: 0 + -44 = -44 -20a + a2 = -44 The a term is -20a. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20a + 100 + a2 = -44 + 100 Reorder the terms: 100 + -20a + a2 = -44 + 100 Combine like terms: -44 + 100 = 56 100 + -20a + a2 = 56 Factor a perfect square on the left side: (a + -10)(a + -10) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (a + -10) equal to 7.483314774 and -7.483314774.Subproblem 1
a + -10 = 7.483314774 Simplifying a + -10 = 7.483314774 Reorder the terms: -10 + a = 7.483314774 Solving -10 + a = 7.483314774 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = 7.483314774 + 10 Combine like terms: -10 + 10 = 0 0 + a = 7.483314774 + 10 a = 7.483314774 + 10 Combine like terms: 7.483314774 + 10 = 17.483314774 a = 17.483314774 Simplifying a = 17.483314774Subproblem 2
a + -10 = -7.483314774 Simplifying a + -10 = -7.483314774 Reorder the terms: -10 + a = -7.483314774 Solving -10 + a = -7.483314774 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = -7.483314774 + 10 Combine like terms: -10 + 10 = 0 0 + a = -7.483314774 + 10 a = -7.483314774 + 10 Combine like terms: -7.483314774 + 10 = 2.516685226 a = 2.516685226 Simplifying a = 2.516685226Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.483314774, 2.516685226}
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