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Simplifying a2 + -10a = 23 Reorder the terms: -10a + a2 = 23 Solving -10a + a2 = 23 Solving for variable 'a'. Reorder the terms: -23 + -10a + a2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -10a + 23 + a2 = 0 + 23 Reorder the terms: -23 + 23 + -10a + a2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -10a + a2 = 0 + 23 -10a + a2 = 0 + 23 Combine like terms: 0 + 23 = 23 -10a + a2 = 23 The a term is -10a. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a + 25 + a2 = 23 + 25 Reorder the terms: 25 + -10a + a2 = 23 + 25 Combine like terms: 23 + 25 = 48 25 + -10a + a2 = 48 Factor a perfect square on the left side: (a + -5)(a + -5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (a + -5) equal to 6.92820323 and -6.92820323.Subproblem 1
a + -5 = 6.92820323 Simplifying a + -5 = 6.92820323 Reorder the terms: -5 + a = 6.92820323 Solving -5 + a = 6.92820323 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + a = 6.92820323 + 5 a = 6.92820323 + 5 Combine like terms: 6.92820323 + 5 = 11.92820323 a = 11.92820323 Simplifying a = 11.92820323Subproblem 2
a + -5 = -6.92820323 Simplifying a + -5 = -6.92820323 Reorder the terms: -5 + a = -6.92820323 Solving -5 + a = -6.92820323 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + a = -6.92820323 + 5 a = -6.92820323 + 5 Combine like terms: -6.92820323 + 5 = -1.92820323 a = -1.92820323 Simplifying a = -1.92820323Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.92820323, -1.92820323}
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