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Simplifying 3a2 + 6a + -24 = 3 Reorder the terms: -24 + 6a + 3a2 = 3 Solving -24 + 6a + 3a2 = 3 Solving for variable 'a'. Reorder the terms: -24 + -3 + 6a + 3a2 = 3 + -3 Combine like terms: -24 + -3 = -27 -27 + 6a + 3a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -27 + 6a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 2a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 2a + a2)' equal to zero and attempt to solve: Simplifying -9 + 2a + a2 = 0 Solving -9 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 2a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + 2a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2a + a2 = 0 + 9 2a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 2a + a2 = 9 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 = 9 + 1 Reorder the terms: 1 + 2a + a2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2a + a2 = 10 Factor a perfect square on the left side: (a + 1)(a + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (a + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
a + 1 = 3.16227766 Simplifying a + 1 = 3.16227766 Reorder the terms: 1 + a = 3.16227766 Solving 1 + a = 3.16227766 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 = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + a = 3.16227766 + -1 a = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 a = 2.16227766 Simplifying a = 2.16227766Subproblem 2
a + 1 = -3.16227766 Simplifying a + 1 = -3.16227766 Reorder the terms: 1 + a = -3.16227766 Solving 1 + a = -3.16227766 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 = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + a = -3.16227766 + -1 a = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 a = -4.16227766 Simplifying a = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.16227766, -4.16227766}Solution
a = {2.16227766, -4.16227766}
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