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Simplifying a2 + -20a + -24 = 0 Reorder the terms: -24 + -20a + a2 = 0 Solving -24 + -20a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -20a + 24 + a2 = 0 + 24 Reorder the terms: -24 + 24 + -20a + a2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -20a + a2 = 0 + 24 -20a + a2 = 0 + 24 Combine like terms: 0 + 24 = 24 -20a + a2 = 24 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 = 24 + 100 Reorder the terms: 100 + -20a + a2 = 24 + 100 Combine like terms: 24 + 100 = 124 100 + -20a + a2 = 124 Factor a perfect square on the left side: (a + -10)(a + -10) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (a + -10) equal to 11.135528726 and -11.135528726.Subproblem 1
a + -10 = 11.135528726 Simplifying a + -10 = 11.135528726 Reorder the terms: -10 + a = 11.135528726 Solving -10 + a = 11.135528726 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 = 11.135528726 + 10 Combine like terms: -10 + 10 = 0 0 + a = 11.135528726 + 10 a = 11.135528726 + 10 Combine like terms: 11.135528726 + 10 = 21.135528726 a = 21.135528726 Simplifying a = 21.135528726Subproblem 2
a + -10 = -11.135528726 Simplifying a + -10 = -11.135528726 Reorder the terms: -10 + a = -11.135528726 Solving -10 + a = -11.135528726 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 = -11.135528726 + 10 Combine like terms: -10 + 10 = 0 0 + a = -11.135528726 + 10 a = -11.135528726 + 10 Combine like terms: -11.135528726 + 10 = -1.135528726 a = -1.135528726 Simplifying a = -1.135528726Solution
The solution to the problem is based on the solutions from the subproblems. a = {21.135528726, -1.135528726}
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