a^2+11a=-1

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Solution for a^2+11a=-1 equation:


Simplifying
a2 + 11a = -1

Reorder the terms:
11a + a2 = -1

Solving
11a + a2 = -1

Solving for variable 'a'.

Reorder the terms:
1 + 11a + a2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 11a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 11a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + 11a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 11a + a2 = 0 + -1
11a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
11a + a2 = -1

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 = -1 + 30.25

Reorder the terms:
30.25 + 11a + a2 = -1 + 30.25

Combine like terms: -1 + 30.25 = 29.25
30.25 + 11a + a2 = 29.25

Factor a perfect square on the left side:
(a + 5.5)(a + 5.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(a + 5.5) equal to 5.408326913 and -5.408326913.

Subproblem 1

a + 5.5 = 5.408326913 Simplifying a + 5.5 = 5.408326913 Reorder the terms: 5.5 + a = 5.408326913 Solving 5.5 + a = 5.408326913 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 = 5.408326913 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 5.408326913 + -5.5 a = 5.408326913 + -5.5 Combine like terms: 5.408326913 + -5.5 = -0.091673087 a = -0.091673087 Simplifying a = -0.091673087

Subproblem 2

a + 5.5 = -5.408326913 Simplifying a + 5.5 = -5.408326913 Reorder the terms: 5.5 + a = -5.408326913 Solving 5.5 + a = -5.408326913 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 = -5.408326913 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -5.408326913 + -5.5 a = -5.408326913 + -5.5 Combine like terms: -5.408326913 + -5.5 = -10.908326913 a = -10.908326913 Simplifying a = -10.908326913

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.091673087, -10.908326913}

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