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Simplifying 9a2 + 18a + -36 = 0 Reorder the terms: -36 + 18a + 9a2 = 0 Solving -36 + 18a + 9a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '9'. 9(-4 + 2a + a2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-4 + 2a + a2)' equal to zero and attempt to solve: Simplifying -4 + 2a + a2 = 0 Solving -4 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 2a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + 2a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2a + a2 = 0 + 4 2a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 2a + a2 = 4 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 4 + 1 Reorder the terms: 1 + 2a + a2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2a + a2 = 5 Factor a perfect square on the left side: (a + 1)(a + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (a + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
a + 1 = 2.236067978 Simplifying a + 1 = 2.236067978 Reorder the terms: 1 + a = 2.236067978 Solving 1 + a = 2.236067978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.236067978 + -1 a = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 a = 1.236067978 Simplifying a = 1.236067978Subproblem 2
a + 1 = -2.236067978 Simplifying a + 1 = -2.236067978 Reorder the terms: 1 + a = -2.236067978 Solving 1 + a = -2.236067978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.236067978 + -1 a = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 a = -3.236067978 Simplifying a = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.236067978, -3.236067978}Solution
a = {1.236067978, -3.236067978}
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