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Simplifying a2 + -9a + -11 = 0 Reorder the terms: -11 + -9a + a2 = 0 Solving -11 + -9a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -9a + 11 + a2 = 0 + 11 Reorder the terms: -11 + 11 + -9a + a2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -9a + a2 = 0 + 11 -9a + a2 = 0 + 11 Combine like terms: 0 + 11 = 11 -9a + a2 = 11 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 = 11 + 20.25 Reorder the terms: 20.25 + -9a + a2 = 11 + 20.25 Combine like terms: 11 + 20.25 = 31.25 20.25 + -9a + a2 = 31.25 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (a + -4.5) equal to 5.590169944 and -5.590169944.Subproblem 1
a + -4.5 = 5.590169944 Simplifying a + -4.5 = 5.590169944 Reorder the terms: -4.5 + a = 5.590169944 Solving -4.5 + a = 5.590169944 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 = 5.590169944 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 5.590169944 + 4.5 a = 5.590169944 + 4.5 Combine like terms: 5.590169944 + 4.5 = 10.090169944 a = 10.090169944 Simplifying a = 10.090169944Subproblem 2
a + -4.5 = -5.590169944 Simplifying a + -4.5 = -5.590169944 Reorder the terms: -4.5 + a = -5.590169944 Solving -4.5 + a = -5.590169944 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 = -5.590169944 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -5.590169944 + 4.5 a = -5.590169944 + 4.5 Combine like terms: -5.590169944 + 4.5 = -1.090169944 a = -1.090169944 Simplifying a = -1.090169944Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.090169944, -1.090169944}
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