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Simplifying a2 + 22a + 5 = 0 Reorder the terms: 5 + 22a + a2 = 0 Solving 5 + 22a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 22a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + 22a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 22a + a2 = 0 + -5 22a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 22a + a2 = -5 The a term is 22a. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22a + 121 + a2 = -5 + 121 Reorder the terms: 121 + 22a + a2 = -5 + 121 Combine like terms: -5 + 121 = 116 121 + 22a + a2 = 116 Factor a perfect square on the left side: (a + 11)(a + 11) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (a + 11) equal to 10.770329614 and -10.770329614.Subproblem 1
a + 11 = 10.770329614 Simplifying a + 11 = 10.770329614 Reorder the terms: 11 + a = 10.770329614 Solving 11 + a = 10.770329614 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + a = 10.770329614 + -11 Combine like terms: 11 + -11 = 0 0 + a = 10.770329614 + -11 a = 10.770329614 + -11 Combine like terms: 10.770329614 + -11 = -0.229670386 a = -0.229670386 Simplifying a = -0.229670386Subproblem 2
a + 11 = -10.770329614 Simplifying a + 11 = -10.770329614 Reorder the terms: 11 + a = -10.770329614 Solving 11 + a = -10.770329614 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + a = -10.770329614 + -11 Combine like terms: 11 + -11 = 0 0 + a = -10.770329614 + -11 a = -10.770329614 + -11 Combine like terms: -10.770329614 + -11 = -21.770329614 a = -21.770329614 Simplifying a = -21.770329614Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.229670386, -21.770329614}
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