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Simplifying 16a = a2 + 10 Reorder the terms: 16a = 10 + a2 Solving 16a = 10 + a2 Solving for variable 'a'. Reorder the terms: -10 + 16a + -1a2 = 10 + a2 + -10 + -1a2 Reorder the terms: -10 + 16a + -1a2 = 10 + -10 + a2 + -1a2 Combine like terms: 10 + -10 = 0 -10 + 16a + -1a2 = 0 + a2 + -1a2 -10 + 16a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -10 + 16a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -16a + a2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -16a + -10 + a2 = 0 + -10 Reorder the terms: 10 + -10 + -16a + a2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -16a + a2 = 0 + -10 -16a + a2 = 0 + -10 Combine like terms: 0 + -10 = -10 -16a + a2 = -10 The a term is -16a. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16a + 64 + a2 = -10 + 64 Reorder the terms: 64 + -16a + a2 = -10 + 64 Combine like terms: -10 + 64 = 54 64 + -16a + a2 = 54 Factor a perfect square on the left side: (a + -8)(a + -8) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (a + -8) equal to 7.348469228 and -7.348469228.Subproblem 1
a + -8 = 7.348469228 Simplifying a + -8 = 7.348469228 Reorder the terms: -8 + a = 7.348469228 Solving -8 + a = 7.348469228 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = 7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + a = 7.348469228 + 8 a = 7.348469228 + 8 Combine like terms: 7.348469228 + 8 = 15.348469228 a = 15.348469228 Simplifying a = 15.348469228Subproblem 2
a + -8 = -7.348469228 Simplifying a + -8 = -7.348469228 Reorder the terms: -8 + a = -7.348469228 Solving -8 + a = -7.348469228 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = -7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + a = -7.348469228 + 8 a = -7.348469228 + 8 Combine like terms: -7.348469228 + 8 = 0.651530772 a = 0.651530772 Simplifying a = 0.651530772Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.348469228, 0.651530772}
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