s^2+10*s+5=0

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Solution for s^2+10*s+5=0 equation:


Simplifying
s2 + 10s + 5 = 0

Reorder the terms:
5 + 10s + s2 = 0

Solving
5 + 10s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 10s + -5 + s2 = 0 + -5

Reorder the terms:
5 + -5 + 10s + s2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 10s + s2 = 0 + -5
10s + s2 = 0 + -5

Combine like terms: 0 + -5 = -5
10s + s2 = -5

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

Add '25' to each side of the equation.
10s + 25 + s2 = -5 + 25

Reorder the terms:
25 + 10s + s2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + 10s + s2 = 20

Factor a perfect square on the left side:
(s + 5)(s + 5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(s + 5) equal to 4.472135955 and -4.472135955.

Subproblem 1

s + 5 = 4.472135955 Simplifying s + 5 = 4.472135955 Reorder the terms: 5 + s = 4.472135955 Solving 5 + s = 4.472135955 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = 4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + s = 4.472135955 + -5 s = 4.472135955 + -5 Combine like terms: 4.472135955 + -5 = -0.527864045 s = -0.527864045 Simplifying s = -0.527864045

Subproblem 2

s + 5 = -4.472135955 Simplifying s + 5 = -4.472135955 Reorder the terms: 5 + s = -4.472135955 Solving 5 + s = -4.472135955 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = -4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + s = -4.472135955 + -5 s = -4.472135955 + -5 Combine like terms: -4.472135955 + -5 = -9.472135955 s = -9.472135955 Simplifying s = -9.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. s = {-0.527864045, -9.472135955}

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