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Simplifying a2 + -24a + -9 = 0 Reorder the terms: -9 + -24a + a2 = 0 Solving -9 + -24a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -24a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + -24a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -24a + a2 = 0 + 9 -24a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 -24a + a2 = 9 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 = 9 + 144 Reorder the terms: 144 + -24a + a2 = 9 + 144 Combine like terms: 9 + 144 = 153 144 + -24a + a2 = 153 Factor a perfect square on the left side: (a + -12)(a + -12) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (a + -12) equal to 12.369316877 and -12.369316877.Subproblem 1
a + -12 = 12.369316877 Simplifying a + -12 = 12.369316877 Reorder the terms: -12 + a = 12.369316877 Solving -12 + a = 12.369316877 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 = 12.369316877 + 12 Combine like terms: -12 + 12 = 0 0 + a = 12.369316877 + 12 a = 12.369316877 + 12 Combine like terms: 12.369316877 + 12 = 24.369316877 a = 24.369316877 Simplifying a = 24.369316877Subproblem 2
a + -12 = -12.369316877 Simplifying a + -12 = -12.369316877 Reorder the terms: -12 + a = -12.369316877 Solving -12 + a = -12.369316877 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 = -12.369316877 + 12 Combine like terms: -12 + 12 = 0 0 + a = -12.369316877 + 12 a = -12.369316877 + 12 Combine like terms: -12.369316877 + 12 = -0.369316877 a = -0.369316877 Simplifying a = -0.369316877Solution
The solution to the problem is based on the solutions from the subproblems. a = {24.369316877, -0.369316877}
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