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Simplifying 3a2 + 12a + -75 = 0 Reorder the terms: -75 + 12a + 3a2 = 0 Solving -75 + 12a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 4a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + 4a + a2)' equal to zero and attempt to solve: Simplifying -25 + 4a + a2 = 0 Solving -25 + 4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 4a + 25 + a2 = 0 + 25 Reorder the terms: -25 + 25 + 4a + a2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4a + a2 = 0 + 25 4a + a2 = 0 + 25 Combine like terms: 0 + 25 = 25 4a + a2 = 25 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 = 25 + 4 Reorder the terms: 4 + 4a + a2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + 4a + a2 = 29 Factor a perfect square on the left side: (a + 2)(a + 2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (a + 2) equal to 5.385164807 and -5.385164807.Subproblem 1
a + 2 = 5.385164807 Simplifying a + 2 = 5.385164807 Reorder the terms: 2 + a = 5.385164807 Solving 2 + a = 5.385164807 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 = 5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + a = 5.385164807 + -2 a = 5.385164807 + -2 Combine like terms: 5.385164807 + -2 = 3.385164807 a = 3.385164807 Simplifying a = 3.385164807Subproblem 2
a + 2 = -5.385164807 Simplifying a + 2 = -5.385164807 Reorder the terms: 2 + a = -5.385164807 Solving 2 + a = -5.385164807 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 = -5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + a = -5.385164807 + -2 a = -5.385164807 + -2 Combine like terms: -5.385164807 + -2 = -7.385164807 a = -7.385164807 Simplifying a = -7.385164807Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.385164807, -7.385164807}Solution
a = {3.385164807, -7.385164807}
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