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Simplifying a2 + -5a + -12 = 0 Reorder the terms: -12 + -5a + a2 = 0 Solving -12 + -5a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -5a + 12 + a2 = 0 + 12 Reorder the terms: -12 + 12 + -5a + a2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5a + a2 = 0 + 12 -5a + a2 = 0 + 12 Combine like terms: 0 + 12 = 12 -5a + a2 = 12 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = 12 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + -5a + a2 = 18.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (a + -2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
a + -2.5 = 4.272001873 Simplifying a + -2.5 = 4.272001873 Reorder the terms: -2.5 + a = 4.272001873 Solving -2.5 + a = 4.272001873 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 4.272001873 + 2.5 a = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 a = 6.772001873 Simplifying a = 6.772001873Subproblem 2
a + -2.5 = -4.272001873 Simplifying a + -2.5 = -4.272001873 Reorder the terms: -2.5 + a = -4.272001873 Solving -2.5 + a = -4.272001873 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -4.272001873 + 2.5 a = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 a = -1.772001873 Simplifying a = -1.772001873Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.772001873, -1.772001873}
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