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Simplifying -1a2 + 12a + -6 = 0 Reorder the terms: -6 + 12a + -1a2 = 0 Solving -6 + 12a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -12a + a2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -12a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + -12a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -12a + a2 = 0 + -6 -12a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -12a + a2 = -6 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 = -6 + 36 Reorder the terms: 36 + -12a + a2 = -6 + 36 Combine like terms: -6 + 36 = 30 36 + -12a + a2 = 30 Factor a perfect square on the left side: (a + -6)(a + -6) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (a + -6) equal to 5.477225575 and -5.477225575.Subproblem 1
a + -6 = 5.477225575 Simplifying a + -6 = 5.477225575 Reorder the terms: -6 + a = 5.477225575 Solving -6 + a = 5.477225575 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 = 5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + a = 5.477225575 + 6 a = 5.477225575 + 6 Combine like terms: 5.477225575 + 6 = 11.477225575 a = 11.477225575 Simplifying a = 11.477225575Subproblem 2
a + -6 = -5.477225575 Simplifying a + -6 = -5.477225575 Reorder the terms: -6 + a = -5.477225575 Solving -6 + a = -5.477225575 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 = -5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + a = -5.477225575 + 6 a = -5.477225575 + 6 Combine like terms: -5.477225575 + 6 = 0.522774425 a = 0.522774425 Simplifying a = 0.522774425Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.477225575, 0.522774425}
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