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Simplifying a2 + -17a + -24 = 0 Reorder the terms: -24 + -17a + a2 = 0 Solving -24 + -17a + 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 + -17a + 24 + a2 = 0 + 24 Reorder the terms: -24 + 24 + -17a + a2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -17a + a2 = 0 + 24 -17a + a2 = 0 + 24 Combine like terms: 0 + 24 = 24 -17a + a2 = 24 The a term is -17a. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17a + 72.25 + a2 = 24 + 72.25 Reorder the terms: 72.25 + -17a + a2 = 24 + 72.25 Combine like terms: 24 + 72.25 = 96.25 72.25 + -17a + a2 = 96.25 Factor a perfect square on the left side: (a + -8.5)(a + -8.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (a + -8.5) equal to 9.810708435 and -9.810708435.Subproblem 1
a + -8.5 = 9.810708435 Simplifying a + -8.5 = 9.810708435 Reorder the terms: -8.5 + a = 9.810708435 Solving -8.5 + a = 9.810708435 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + a = 9.810708435 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + a = 9.810708435 + 8.5 a = 9.810708435 + 8.5 Combine like terms: 9.810708435 + 8.5 = 18.310708435 a = 18.310708435 Simplifying a = 18.310708435Subproblem 2
a + -8.5 = -9.810708435 Simplifying a + -8.5 = -9.810708435 Reorder the terms: -8.5 + a = -9.810708435 Solving -8.5 + a = -9.810708435 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + a = -9.810708435 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + a = -9.810708435 + 8.5 a = -9.810708435 + 8.5 Combine like terms: -9.810708435 + 8.5 = -1.310708435 a = -1.310708435 Simplifying a = -1.310708435Solution
The solution to the problem is based on the solutions from the subproblems. a = {18.310708435, -1.310708435}
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