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Simplifying 3a + -4 = a2 + -3a Reorder the terms: -4 + 3a = a2 + -3a Reorder the terms: -4 + 3a = -3a + a2 Solving -4 + 3a = -3a + a2 Solving for variable 'a'. Combine like terms: 3a + 3a = 6a -4 + 6a + -1a2 = -3a + a2 + 3a + -1a2 Reorder the terms: -4 + 6a + -1a2 = -3a + 3a + a2 + -1a2 Combine like terms: -3a + 3a = 0 -4 + 6a + -1a2 = 0 + a2 + -1a2 -4 + 6a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -4 + 6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -6a + a2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -6a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6a + a2 = 0 + -4 -6a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6a + a2 = -4 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 = -4 + 9 Reorder the terms: 9 + -6a + a2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6a + a2 = 5 Factor a perfect square on the left side: (a + -3)(a + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (a + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
a + -3 = 2.236067978 Simplifying a + -3 = 2.236067978 Reorder the terms: -3 + a = 2.236067978 Solving -3 + a = 2.236067978 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 = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.236067978 + 3 a = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 a = 5.236067978 Simplifying a = 5.236067978Subproblem 2
a + -3 = -2.236067978 Simplifying a + -3 = -2.236067978 Reorder the terms: -3 + a = -2.236067978 Solving -3 + a = -2.236067978 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 = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.236067978 + 3 a = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 a = 0.763932022 Simplifying a = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.236067978, 0.763932022}
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