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Simplifying 3a2 = -9a + 9 Reorder the terms: 3a2 = 9 + -9a Solving 3a2 = 9 + -9a Solving for variable 'a'. Reorder the terms: -9 + 9a + 3a2 = 9 + -9a + -9 + 9a Reorder the terms: -9 + 9a + 3a2 = 9 + -9 + -9a + 9a Combine like terms: 9 + -9 = 0 -9 + 9a + 3a2 = 0 + -9a + 9a -9 + 9a + 3a2 = -9a + 9a Combine like terms: -9a + 9a = 0 -9 + 9a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 3a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 3a + a2)' equal to zero and attempt to solve: Simplifying -3 + 3a + a2 = 0 Solving -3 + 3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 3a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + 3a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3a + a2 = 0 + 3 3a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 3a + a2 = 3 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = 3 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + 3a + a2 = 5.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (a + 1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
a + 1.5 = 2.291287847 Simplifying a + 1.5 = 2.291287847 Reorder the terms: 1.5 + a = 2.291287847 Solving 1.5 + a = 2.291287847 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 2.291287847 + -1.5 a = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 a = 0.791287847 Simplifying a = 0.791287847Subproblem 2
a + 1.5 = -2.291287847 Simplifying a + 1.5 = -2.291287847 Reorder the terms: 1.5 + a = -2.291287847 Solving 1.5 + a = -2.291287847 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -2.291287847 + -1.5 a = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 a = -3.791287847 Simplifying a = -3.791287847Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.791287847, -3.791287847}Solution
a = {0.791287847, -3.791287847}
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