a^2+10a+11=0

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Solution for a^2+10a+11=0 equation:


Simplifying
a2 + 10a + 11 = 0

Reorder the terms:
11 + 10a + a2 = 0

Solving
11 + 10a + 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 + 10a + -11 + a2 = 0 + -11

Reorder the terms:
11 + -11 + 10a + a2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 10a + a2 = 0 + -11
10a + a2 = 0 + -11

Combine like terms: 0 + -11 = -11
10a + a2 = -11

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = -11 + 25

Reorder the terms:
25 + 10a + a2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + 10a + a2 = 14

Factor a perfect square on the left side:
(a + 5)(a + 5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(a + 5) equal to 3.741657387 and -3.741657387.

Subproblem 1

a + 5 = 3.741657387 Simplifying a + 5 = 3.741657387 Reorder the terms: 5 + a = 3.741657387 Solving 5 + a = 3.741657387 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + a = 3.741657387 + -5 a = 3.741657387 + -5 Combine like terms: 3.741657387 + -5 = -1.258342613 a = -1.258342613 Simplifying a = -1.258342613

Subproblem 2

a + 5 = -3.741657387 Simplifying a + 5 = -3.741657387 Reorder the terms: 5 + a = -3.741657387 Solving 5 + a = -3.741657387 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + a = -3.741657387 + -5 a = -3.741657387 + -5 Combine like terms: -3.741657387 + -5 = -8.741657387 a = -8.741657387 Simplifying a = -8.741657387

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-1.258342613, -8.741657387}

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