5s^2+11s-11=0

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Solution for 5s^2+11s-11=0 equation:


Simplifying
5s2 + 11s + -11 = 0

Reorder the terms:
-11 + 11s + 5s2 = 0

Solving
-11 + 11s + 5s2 = 0

Solving for variable 's'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-2.2 + 2.2s + s2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 2.2s + 2.2 + s2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 2.2s + s2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 2.2s + s2 = 0 + 2.2
2.2s + s2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
2.2s + s2 = 2.2

The s term is 2.2s.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2s + 1.21 + s2 = 2.2 + 1.21

Reorder the terms:
1.21 + 2.2s + s2 = 2.2 + 1.21

Combine like terms: 2.2 + 1.21 = 3.41
1.21 + 2.2s + s2 = 3.41

Factor a perfect square on the left side:
(s + 1.1)(s + 1.1) = 3.41

Calculate the square root of the right side: 1.846618531

Break this problem into two subproblems by setting 
(s + 1.1) equal to 1.846618531 and -1.846618531.

Subproblem 1

s + 1.1 = 1.846618531 Simplifying s + 1.1 = 1.846618531 Reorder the terms: 1.1 + s = 1.846618531 Solving 1.1 + s = 1.846618531 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + s = 1.846618531 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + s = 1.846618531 + -1.1 s = 1.846618531 + -1.1 Combine like terms: 1.846618531 + -1.1 = 0.746618531 s = 0.746618531 Simplifying s = 0.746618531

Subproblem 2

s + 1.1 = -1.846618531 Simplifying s + 1.1 = -1.846618531 Reorder the terms: 1.1 + s = -1.846618531 Solving 1.1 + s = -1.846618531 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + s = -1.846618531 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + s = -1.846618531 + -1.1 s = -1.846618531 + -1.1 Combine like terms: -1.846618531 + -1.1 = -2.946618531 s = -2.946618531 Simplifying s = -2.946618531

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.746618531, -2.946618531}

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