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Simplifying a2 + -24a = 16 Reorder the terms: -24a + a2 = 16 Solving -24a + a2 = 16 Solving for variable 'a'. Reorder the terms: -16 + -24a + a2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -24a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -24a + 16 + a2 = 0 + 16 Reorder the terms: -16 + 16 + -24a + a2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -24a + a2 = 0 + 16 -24a + a2 = 0 + 16 Combine like terms: 0 + 16 = 16 -24a + a2 = 16 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 = 16 + 144 Reorder the terms: 144 + -24a + a2 = 16 + 144 Combine like terms: 16 + 144 = 160 144 + -24a + a2 = 160 Factor a perfect square on the left side: (a + -12)(a + -12) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (a + -12) equal to 12.649110641 and -12.649110641.Subproblem 1
a + -12 = 12.649110641 Simplifying a + -12 = 12.649110641 Reorder the terms: -12 + a = 12.649110641 Solving -12 + a = 12.649110641 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 = 12.649110641 + 12 Combine like terms: -12 + 12 = 0 0 + a = 12.649110641 + 12 a = 12.649110641 + 12 Combine like terms: 12.649110641 + 12 = 24.649110641 a = 24.649110641 Simplifying a = 24.649110641Subproblem 2
a + -12 = -12.649110641 Simplifying a + -12 = -12.649110641 Reorder the terms: -12 + a = -12.649110641 Solving -12 + a = -12.649110641 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 = -12.649110641 + 12 Combine like terms: -12 + 12 = 0 0 + a = -12.649110641 + 12 a = -12.649110641 + 12 Combine like terms: -12.649110641 + 12 = -0.649110641 a = -0.649110641 Simplifying a = -0.649110641Solution
The solution to the problem is based on the solutions from the subproblems. a = {24.649110641, -0.649110641}
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