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Simplifying 3a2 + -18a + 5 = 0 Reorder the terms: 5 + -18a + 3a2 = 0 Solving 5 + -18a + 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'. 1.666666667 + -6a + a2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -6a + -1.666666667 + a2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -6a + a2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -6a + a2 = 0 + -1.666666667 -6a + a2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -6a + a2 = -1.666666667 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = -1.666666667 + 9 Reorder the terms: 9 + -6a + a2 = -1.666666667 + 9 Combine like terms: -1.666666667 + 9 = 7.333333333 9 + -6a + a2 = 7.333333333 Factor a perfect square on the left side: (a + -3)(a + -3) = 7.333333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (a + -3) equal to 2.708012801 and -2.708012801.Subproblem 1
a + -3 = 2.708012801 Simplifying a + -3 = 2.708012801 Reorder the terms: -3 + a = 2.708012801 Solving -3 + a = 2.708012801 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 2.708012801 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.708012801 + 3 a = 2.708012801 + 3 Combine like terms: 2.708012801 + 3 = 5.708012801 a = 5.708012801 Simplifying a = 5.708012801Subproblem 2
a + -3 = -2.708012801 Simplifying a + -3 = -2.708012801 Reorder the terms: -3 + a = -2.708012801 Solving -3 + a = -2.708012801 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -2.708012801 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.708012801 + 3 a = -2.708012801 + 3 Combine like terms: -2.708012801 + 3 = 0.291987199 a = 0.291987199 Simplifying a = 0.291987199Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.708012801, 0.291987199}
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