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Simplifying 4a2 + -8a = 16 Reorder the terms: -8a + 4a2 = 16 Solving -8a + 4a2 = 16 Solving for variable 'a'. Reorder the terms: -16 + -8a + 4a2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -8a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -2a + a2) = 0 Ignore the factor 4.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 = 3.236067978 a = 3.236067978 Simplifying a = 3.236067978Subproblem 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 = -1.236067978 a = -1.236067978 Simplifying a = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.236067978, -1.236067978}Solution
a = {3.236067978, -1.236067978}
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