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Simplifying 4a2 + 8a = 24 Reorder the terms: 8a + 4a2 = 24 Solving 8a + 4a2 = 24 Solving for variable 'a'. Reorder the terms: -24 + 8a + 4a2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 8a + 4a2 = 0 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 = 1.645751311 a = 1.645751311 Simplifying a = 1.645751311Subproblem 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 = -3.645751311 a = -3.645751311 Simplifying a = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.645751311, -3.645751311}Solution
a = {1.645751311, -3.645751311}
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