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Simplifying a2 + 24a + -200 = 0 Reorder the terms: -200 + 24a + a2 = 0 Solving -200 + 24a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 24a + 200 + a2 = 0 + 200 Reorder the terms: -200 + 200 + 24a + a2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 24a + a2 = 0 + 200 24a + a2 = 0 + 200 Combine like terms: 0 + 200 = 200 24a + a2 = 200 The a term is 24a. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24a + 144 + a2 = 200 + 144 Reorder the terms: 144 + 24a + a2 = 200 + 144 Combine like terms: 200 + 144 = 344 144 + 24a + a2 = 344 Factor a perfect square on the left side: (a + 12)(a + 12) = 344 Calculate the square root of the right side: 18.547236991 Break this problem into two subproblems by setting (a + 12) equal to 18.547236991 and -18.547236991.Subproblem 1
a + 12 = 18.547236991 Simplifying a + 12 = 18.547236991 Reorder the terms: 12 + a = 18.547236991 Solving 12 + a = 18.547236991 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + a = 18.547236991 + -12 Combine like terms: 12 + -12 = 0 0 + a = 18.547236991 + -12 a = 18.547236991 + -12 Combine like terms: 18.547236991 + -12 = 6.547236991 a = 6.547236991 Simplifying a = 6.547236991Subproblem 2
a + 12 = -18.547236991 Simplifying a + 12 = -18.547236991 Reorder the terms: 12 + a = -18.547236991 Solving 12 + a = -18.547236991 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + a = -18.547236991 + -12 Combine like terms: 12 + -12 = 0 0 + a = -18.547236991 + -12 a = -18.547236991 + -12 Combine like terms: -18.547236991 + -12 = -30.547236991 a = -30.547236991 Simplifying a = -30.547236991Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.547236991, -30.547236991}
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