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Simplifying 2a(a + 4) = 26 Reorder the terms: 2a(4 + a) = 26 (4 * 2a + a * 2a) = 26 (8a + 2a2) = 26 Solving 8a + 2a2 = 26 Solving for variable 'a'. Reorder the terms: -26 + 8a + 2a2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 8a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 4a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 4a + a2)' equal to zero and attempt to solve: Simplifying -13 + 4a + a2 = 0 Solving -13 + 4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 4a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + 4a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4a + a2 = 0 + 13 4a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 4a + a2 = 13 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 13 + 4 Reorder the terms: 4 + 4a + a2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + 4a + a2 = 17 Factor a perfect square on the left side: (a + 2)(a + 2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (a + 2) equal to 4.123105626 and -4.123105626.Subproblem 1
a + 2 = 4.123105626 Simplifying a + 2 = 4.123105626 Reorder the terms: 2 + a = 4.123105626 Solving 2 + a = 4.123105626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + a = 4.123105626 + -2 a = 4.123105626 + -2 Combine like terms: 4.123105626 + -2 = 2.123105626 a = 2.123105626 Simplifying a = 2.123105626Subproblem 2
a + 2 = -4.123105626 Simplifying a + 2 = -4.123105626 Reorder the terms: 2 + a = -4.123105626 Solving 2 + a = -4.123105626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + a = -4.123105626 + -2 a = -4.123105626 + -2 Combine like terms: -4.123105626 + -2 = -6.123105626 a = -6.123105626 Simplifying a = -6.123105626Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.123105626, -6.123105626}Solution
a = {2.123105626, -6.123105626}
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