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Simplifying a2 + -12a + -16 = 0 Reorder the terms: -16 + -12a + a2 = 0 Solving -16 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -12a + 16 + a2 = 0 + 16 Reorder the terms: -16 + 16 + -12a + a2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -12a + a2 = 0 + 16 -12a + a2 = 0 + 16 Combine like terms: 0 + 16 = 16 -12a + a2 = 16 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = 16 + 36 Reorder the terms: 36 + -12a + a2 = 16 + 36 Combine like terms: 16 + 36 = 52 36 + -12a + a2 = 52 Factor a perfect square on the left side: (a + -6)(a + -6) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (a + -6) equal to 7.211102551 and -7.211102551.Subproblem 1
a + -6 = 7.211102551 Simplifying a + -6 = 7.211102551 Reorder the terms: -6 + a = 7.211102551 Solving -6 + a = 7.211102551 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + a = 7.211102551 + 6 a = 7.211102551 + 6 Combine like terms: 7.211102551 + 6 = 13.211102551 a = 13.211102551 Simplifying a = 13.211102551Subproblem 2
a + -6 = -7.211102551 Simplifying a + -6 = -7.211102551 Reorder the terms: -6 + a = -7.211102551 Solving -6 + a = -7.211102551 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + a = -7.211102551 + 6 a = -7.211102551 + 6 Combine like terms: -7.211102551 + 6 = -1.211102551 a = -1.211102551 Simplifying a = -1.211102551Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.211102551, -1.211102551}
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