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Simplifying 2a(a + 10) + 44 = 180 Reorder the terms: 2a(10 + a) + 44 = 180 (10 * 2a + a * 2a) + 44 = 180 (20a + 2a2) + 44 = 180 Reorder the terms: 44 + 20a + 2a2 = 180 Solving 44 + 20a + 2a2 = 180 Solving for variable 'a'. Reorder the terms: 44 + -180 + 20a + 2a2 = 180 + -180 Combine like terms: 44 + -180 = -136 -136 + 20a + 2a2 = 180 + -180 Combine like terms: 180 + -180 = 0 -136 + 20a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-68 + 10a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-68 + 10a + a2)' equal to zero and attempt to solve: Simplifying -68 + 10a + a2 = 0 Solving -68 + 10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 10a + 68 + a2 = 0 + 68 Reorder the terms: -68 + 68 + 10a + a2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 10a + a2 = 0 + 68 10a + a2 = 0 + 68 Combine like terms: 0 + 68 = 68 10a + a2 = 68 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = 68 + 25 Reorder the terms: 25 + 10a + a2 = 68 + 25 Combine like terms: 68 + 25 = 93 25 + 10a + a2 = 93 Factor a perfect square on the left side: (a + 5)(a + 5) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (a + 5) equal to 9.643650761 and -9.643650761.Subproblem 1
a + 5 = 9.643650761 Simplifying a + 5 = 9.643650761 Reorder the terms: 5 + a = 9.643650761 Solving 5 + a = 9.643650761 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 9.643650761 + -5 Combine like terms: 5 + -5 = 0 0 + a = 9.643650761 + -5 a = 9.643650761 + -5 Combine like terms: 9.643650761 + -5 = 4.643650761 a = 4.643650761 Simplifying a = 4.643650761Subproblem 2
a + 5 = -9.643650761 Simplifying a + 5 = -9.643650761 Reorder the terms: 5 + a = -9.643650761 Solving 5 + a = -9.643650761 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -9.643650761 + -5 Combine like terms: 5 + -5 = 0 0 + a = -9.643650761 + -5 a = -9.643650761 + -5 Combine like terms: -9.643650761 + -5 = -14.643650761 a = -14.643650761 Simplifying a = -14.643650761Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.643650761, -14.643650761}Solution
a = {4.643650761, -14.643650761}
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