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Simplifying a2 + -9a + -6 = 0 Reorder the terms: -6 + -9a + a2 = 0 Solving -6 + -9a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -9a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -9a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -9a + a2 = 0 + 6 -9a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -9a + a2 = 6 The a term is -9a. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9a + 20.25 + a2 = 6 + 20.25 Reorder the terms: 20.25 + -9a + a2 = 6 + 20.25 Combine like terms: 6 + 20.25 = 26.25 20.25 + -9a + a2 = 26.25 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (a + -4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
a + -4.5 = 5.123475383 Simplifying a + -4.5 = 5.123475383 Reorder the terms: -4.5 + a = 5.123475383 Solving -4.5 + a = 5.123475383 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = 5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 5.123475383 + 4.5 a = 5.123475383 + 4.5 Combine like terms: 5.123475383 + 4.5 = 9.623475383 a = 9.623475383 Simplifying a = 9.623475383Subproblem 2
a + -4.5 = -5.123475383 Simplifying a + -4.5 = -5.123475383 Reorder the terms: -4.5 + a = -5.123475383 Solving -4.5 + a = -5.123475383 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = -5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -5.123475383 + 4.5 a = -5.123475383 + 4.5 Combine like terms: -5.123475383 + 4.5 = -0.623475383 a = -0.623475383 Simplifying a = -0.623475383Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.623475383, -0.623475383}
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