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Simplifying a2 + 11a + -51 = 0 Reorder the terms: -51 + 11a + a2 = 0 Solving -51 + 11a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 11a + 51 + a2 = 0 + 51 Reorder the terms: -51 + 51 + 11a + a2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 11a + a2 = 0 + 51 11a + a2 = 0 + 51 Combine like terms: 0 + 51 = 51 11a + a2 = 51 The a term is 11a. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11a + 30.25 + a2 = 51 + 30.25 Reorder the terms: 30.25 + 11a + a2 = 51 + 30.25 Combine like terms: 51 + 30.25 = 81.25 30.25 + 11a + a2 = 81.25 Factor a perfect square on the left side: (a + 5.5)(a + 5.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (a + 5.5) equal to 9.013878189 and -9.013878189.Subproblem 1
a + 5.5 = 9.013878189 Simplifying a + 5.5 = 9.013878189 Reorder the terms: 5.5 + a = 9.013878189 Solving 5.5 + a = 9.013878189 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = 9.013878189 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 9.013878189 + -5.5 a = 9.013878189 + -5.5 Combine like terms: 9.013878189 + -5.5 = 3.513878189 a = 3.513878189 Simplifying a = 3.513878189Subproblem 2
a + 5.5 = -9.013878189 Simplifying a + 5.5 = -9.013878189 Reorder the terms: 5.5 + a = -9.013878189 Solving 5.5 + a = -9.013878189 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = -9.013878189 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -9.013878189 + -5.5 a = -9.013878189 + -5.5 Combine like terms: -9.013878189 + -5.5 = -14.513878189 a = -14.513878189 Simplifying a = -14.513878189Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.513878189, -14.513878189}
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