a^2+10a+1=0

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Solution for a^2+10a+1=0 equation:


Simplifying
a2 + 10a + 1 = 0

Reorder the terms:
1 + 10a + a2 = 0

Solving
1 + 10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 10a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + 10a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10a + a2 = 0 + -1
10a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
10a + a2 = -1

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 = -1 + 25

Reorder the terms:
25 + 10a + a2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + 10a + a2 = 24

Factor a perfect square on the left side:
(a + 5)(a + 5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(a + 5) equal to 4.898979486 and -4.898979486.

Subproblem 1

a + 5 = 4.898979486 Simplifying a + 5 = 4.898979486 Reorder the terms: 5 + a = 4.898979486 Solving 5 + a = 4.898979486 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 = 4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + a = 4.898979486 + -5 a = 4.898979486 + -5 Combine like terms: 4.898979486 + -5 = -0.101020514 a = -0.101020514 Simplifying a = -0.101020514

Subproblem 2

a + 5 = -4.898979486 Simplifying a + 5 = -4.898979486 Reorder the terms: 5 + a = -4.898979486 Solving 5 + a = -4.898979486 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 = -4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + a = -4.898979486 + -5 a = -4.898979486 + -5 Combine like terms: -4.898979486 + -5 = -9.898979486 a = -9.898979486 Simplifying a = -9.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.101020514, -9.898979486}

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