5s^2-4s-4=0

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Solution for 5s^2-4s-4=0 equation:


Simplifying
5s2 + -4s + -4 = 0

Reorder the terms:
-4 + -4s + 5s2 = 0

Solving
-4 + -4s + 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'.
-0.8 + -0.8s + s2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -0.8s + 0.8 + s2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -0.8s + s2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -0.8s + s2 = 0 + 0.8
-0.8s + s2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-0.8s + s2 = 0.8

The s term is -0.8s.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8s + 0.16 + s2 = 0.8 + 0.16

Reorder the terms:
0.16 + -0.8s + s2 = 0.8 + 0.16

Combine like terms: 0.8 + 0.16 = 0.96
0.16 + -0.8s + s2 = 0.96

Factor a perfect square on the left side:
(s + -0.4)(s + -0.4) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(s + -0.4) equal to 0.979795897 and -0.979795897.

Subproblem 1

s + -0.4 = 0.979795897 Simplifying s + -0.4 = 0.979795897 Reorder the terms: -0.4 + s = 0.979795897 Solving -0.4 + s = 0.979795897 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + s = 0.979795897 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + s = 0.979795897 + 0.4 s = 0.979795897 + 0.4 Combine like terms: 0.979795897 + 0.4 = 1.379795897 s = 1.379795897 Simplifying s = 1.379795897

Subproblem 2

s + -0.4 = -0.979795897 Simplifying s + -0.4 = -0.979795897 Reorder the terms: -0.4 + s = -0.979795897 Solving -0.4 + s = -0.979795897 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + s = -0.979795897 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + s = -0.979795897 + 0.4 s = -0.979795897 + 0.4 Combine like terms: -0.979795897 + 0.4 = -0.579795897 s = -0.579795897 Simplifying s = -0.579795897

Solution

The solution to the problem is based on the solutions from the subproblems. s = {1.379795897, -0.579795897}

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