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Simplifying 4a2 + -8a + -24 = 0 Reorder the terms: -24 + -8a + 4a2 = 0 Solving -24 + -8a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -2a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -2a + a2)' equal to zero and attempt to solve: Simplifying -6 + -2a + a2 = 0 Solving -6 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -2a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -2a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2a + a2 = 0 + 6 -2a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2a + a2 = 6 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 = 6 + 1 Reorder the terms: 1 + -2a + a2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2a + a2 = 7 Factor a perfect square on the left side: (a + -1)(a + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (a + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
a + -1 = 2.645751311 Simplifying a + -1 = 2.645751311 Reorder the terms: -1 + a = 2.645751311 Solving -1 + a = 2.645751311 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 = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.645751311 + 1 a = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 a = 3.645751311 Simplifying a = 3.645751311Subproblem 2
a + -1 = -2.645751311 Simplifying a + -1 = -2.645751311 Reorder the terms: -1 + a = -2.645751311 Solving -1 + a = -2.645751311 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 = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.645751311 + 1 a = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 a = -1.645751311 Simplifying a = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.645751311, -1.645751311}Solution
a = {3.645751311, -1.645751311}
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