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Simplifying -2a2 + 36a + -4a + -44 = 0 Reorder the terms: -44 + 36a + -4a + -2a2 = 0 Combine like terms: 36a + -4a = 32a -44 + 32a + -2a2 = 0 Solving -44 + 32a + -2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 16a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 16a + -1a2)' equal to zero and attempt to solve: Simplifying -22 + 16a + -1a2 = 0 Solving -22 + 16a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 22 + -16a + a2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -16a + -22 + a2 = 0 + -22 Reorder the terms: 22 + -22 + -16a + a2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -16a + a2 = 0 + -22 -16a + a2 = 0 + -22 Combine like terms: 0 + -22 = -22 -16a + a2 = -22 The a term is -16a. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16a + 64 + a2 = -22 + 64 Reorder the terms: 64 + -16a + a2 = -22 + 64 Combine like terms: -22 + 64 = 42 64 + -16a + a2 = 42 Factor a perfect square on the left side: (a + -8)(a + -8) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (a + -8) equal to 6.480740698 and -6.480740698.Subproblem 1
a + -8 = 6.480740698 Simplifying a + -8 = 6.480740698 Reorder the terms: -8 + a = 6.480740698 Solving -8 + a = 6.480740698 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = 6.480740698 + 8 Combine like terms: -8 + 8 = 0 0 + a = 6.480740698 + 8 a = 6.480740698 + 8 Combine like terms: 6.480740698 + 8 = 14.480740698 a = 14.480740698 Simplifying a = 14.480740698Subproblem 2
a + -8 = -6.480740698 Simplifying a + -8 = -6.480740698 Reorder the terms: -8 + a = -6.480740698 Solving -8 + a = -6.480740698 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = -6.480740698 + 8 Combine like terms: -8 + 8 = 0 0 + a = -6.480740698 + 8 a = -6.480740698 + 8 Combine like terms: -6.480740698 + 8 = 1.519259302 a = 1.519259302 Simplifying a = 1.519259302Solution
The solution to the problem is based on the solutions from the subproblems. a = {14.480740698, 1.519259302}Solution
a = {14.480740698, 1.519259302}
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