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Simplifying a2 + -12a + 3 = 0 Reorder the terms: 3 + -12a + a2 = 0 Solving 3 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -12a + -3 + a2 = 0 + -3 Reorder the terms: 3 + -3 + -12a + a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -12a + a2 = 0 + -3 -12a + a2 = 0 + -3 Combine like terms: 0 + -3 = -3 -12a + a2 = -3 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 = -3 + 36 Reorder the terms: 36 + -12a + a2 = -3 + 36 Combine like terms: -3 + 36 = 33 36 + -12a + a2 = 33 Factor a perfect square on the left side: (a + -6)(a + -6) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (a + -6) equal to 5.744562647 and -5.744562647.Subproblem 1
a + -6 = 5.744562647 Simplifying a + -6 = 5.744562647 Reorder the terms: -6 + a = 5.744562647 Solving -6 + a = 5.744562647 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 = 5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + a = 5.744562647 + 6 a = 5.744562647 + 6 Combine like terms: 5.744562647 + 6 = 11.744562647 a = 11.744562647 Simplifying a = 11.744562647Subproblem 2
a + -6 = -5.744562647 Simplifying a + -6 = -5.744562647 Reorder the terms: -6 + a = -5.744562647 Solving -6 + a = -5.744562647 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 = -5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + a = -5.744562647 + 6 a = -5.744562647 + 6 Combine like terms: -5.744562647 + 6 = 0.255437353 a = 0.255437353 Simplifying a = 0.255437353Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.744562647, 0.255437353}
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