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Simplifying 3a2 + -36a + 86 = 0 Reorder the terms: 86 + -36a + 3a2 = 0 Solving 86 + -36a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 28.66666667 + -12a + a2 = 0 Move the constant term to the right: Add '-28.66666667' to each side of the equation. 28.66666667 + -12a + -28.66666667 + a2 = 0 + -28.66666667 Reorder the terms: 28.66666667 + -28.66666667 + -12a + a2 = 0 + -28.66666667 Combine like terms: 28.66666667 + -28.66666667 = 0.00000000 0.00000000 + -12a + a2 = 0 + -28.66666667 -12a + a2 = 0 + -28.66666667 Combine like terms: 0 + -28.66666667 = -28.66666667 -12a + a2 = -28.66666667 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 = -28.66666667 + 36 Reorder the terms: 36 + -12a + a2 = -28.66666667 + 36 Combine like terms: -28.66666667 + 36 = 7.33333333 36 + -12a + a2 = 7.33333333 Factor a perfect square on the left side: (a + -6)(a + -6) = 7.33333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (a + -6) equal to 2.708012801 and -2.708012801.Subproblem 1
a + -6 = 2.708012801 Simplifying a + -6 = 2.708012801 Reorder the terms: -6 + a = 2.708012801 Solving -6 + a = 2.708012801 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 = 2.708012801 + 6 Combine like terms: -6 + 6 = 0 0 + a = 2.708012801 + 6 a = 2.708012801 + 6 Combine like terms: 2.708012801 + 6 = 8.708012801 a = 8.708012801 Simplifying a = 8.708012801Subproblem 2
a + -6 = -2.708012801 Simplifying a + -6 = -2.708012801 Reorder the terms: -6 + a = -2.708012801 Solving -6 + a = -2.708012801 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 = -2.708012801 + 6 Combine like terms: -6 + 6 = 0 0 + a = -2.708012801 + 6 a = -2.708012801 + 6 Combine like terms: -2.708012801 + 6 = 3.291987199 a = 3.291987199 Simplifying a = 3.291987199Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.708012801, 3.291987199}
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