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Simplifying a(a + -4) = 4a + -1(2a + 4) Reorder the terms: a(-4 + a) = 4a + -1(2a + 4) (-4 * a + a * a) = 4a + -1(2a + 4) (-4a + a2) = 4a + -1(2a + 4) Reorder the terms: -4a + a2 = 4a + -1(4 + 2a) -4a + a2 = 4a + (4 * -1 + 2a * -1) -4a + a2 = 4a + (-4 + -2a) Reorder the terms: -4a + a2 = -4 + 4a + -2a Combine like terms: 4a + -2a = 2a -4a + a2 = -4 + 2a Solving -4a + a2 = -4 + 2a Solving for variable 'a'. Reorder the terms: 4 + -4a + -2a + a2 = -4 + 2a + 4 + -2a Combine like terms: -4a + -2a = -6a 4 + -6a + a2 = -4 + 2a + 4 + -2a Reorder the terms: 4 + -6a + a2 = -4 + 4 + 2a + -2a Combine like terms: -4 + 4 = 0 4 + -6a + a2 = 0 + 2a + -2a 4 + -6a + a2 = 2a + -2a Combine like terms: 2a + -2a = 0 4 + -6a + a2 = 0 Begin completing the square. 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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