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Simplifying 2a2 + -8a + -16 = 10 Reorder the terms: -16 + -8a + 2a2 = 10 Solving -16 + -8a + 2a2 = 10 Solving for variable 'a'. Reorder the terms: -16 + -10 + -8a + 2a2 = 10 + -10 Combine like terms: -16 + -10 = -26 -26 + -8a + 2a2 = 10 + -10 Combine like terms: 10 + -10 = 0 -26 + -8a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -4a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -4a + a2)' equal to zero and attempt to solve: Simplifying -13 + -4a + a2 = 0 Solving -13 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + -4a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4a + a2 = 0 + 13 -4a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4a + a2 = 13 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 = 13 + 4 Reorder the terms: 4 + -4a + a2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4a + a2 = 17 Factor a perfect square on the left side: (a + -2)(a + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (a + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
a + -2 = 4.123105626 Simplifying a + -2 = 4.123105626 Reorder the terms: -2 + a = 4.123105626 Solving -2 + a = 4.123105626 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 = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + a = 4.123105626 + 2 a = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 a = 6.123105626 Simplifying a = 6.123105626Subproblem 2
a + -2 = -4.123105626 Simplifying a + -2 = -4.123105626 Reorder the terms: -2 + a = -4.123105626 Solving -2 + a = -4.123105626 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 = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + a = -4.123105626 + 2 a = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 a = -2.123105626 Simplifying a = -2.123105626Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.123105626, -2.123105626}Solution
a = {6.123105626, -2.123105626}
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