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Simplifying 3a(a + -4) = 27 Reorder the terms: 3a(-4 + a) = 27 (-4 * 3a + a * 3a) = 27 (-12a + 3a2) = 27 Solving -12a + 3a2 = 27 Solving for variable 'a'. Reorder the terms: -27 + -12a + 3a2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -12a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -4a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + -4a + a2)' equal to zero and attempt to solve: Simplifying -9 + -4a + a2 = 0 Solving -9 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + -4a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4a + a2 = 0 + 9 -4a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4a + a2 = 9 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 = 9 + 4 Reorder the terms: 4 + -4a + a2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4a + a2 = 13 Factor a perfect square on the left side: (a + -2)(a + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (a + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
a + -2 = 3.605551275 Simplifying a + -2 = 3.605551275 Reorder the terms: -2 + a = 3.605551275 Solving -2 + a = 3.605551275 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 = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + a = 3.605551275 + 2 a = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 a = 5.605551275 Simplifying a = 5.605551275Subproblem 2
a + -2 = -3.605551275 Simplifying a + -2 = -3.605551275 Reorder the terms: -2 + a = -3.605551275 Solving -2 + a = -3.605551275 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 = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + a = -3.605551275 + 2 a = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 a = -1.605551275 Simplifying a = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.605551275, -1.605551275}Solution
a = {5.605551275, -1.605551275}
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