5s^2+4s-2=0

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


Simplifying
5s2 + 4s + -2 = 0

Reorder the terms:
-2 + 4s + 5s2 = 0

Solving
-2 + 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'.
-0.4 + 0.8s + s2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.8s + 0.4 + s2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.8s + s2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.8s + s2 = 0 + 0.4
0.8s + s2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.8s + s2 = 0.4

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 = 0.4 + 0.16

Reorder the terms:
0.16 + 0.8s + s2 = 0.4 + 0.16

Combine like terms: 0.4 + 0.16 = 0.56
0.16 + 0.8s + s2 = 0.56

Factor a perfect square on the left side:
(s + 0.4)(s + 0.4) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(s + 0.4) equal to 0.748331477 and -0.748331477.

Subproblem 1

s + 0.4 = 0.748331477 Simplifying s + 0.4 = 0.748331477 Reorder the terms: 0.4 + s = 0.748331477 Solving 0.4 + s = 0.748331477 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 = 0.748331477 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + s = 0.748331477 + -0.4 s = 0.748331477 + -0.4 Combine like terms: 0.748331477 + -0.4 = 0.348331477 s = 0.348331477 Simplifying s = 0.348331477

Subproblem 2

s + 0.4 = -0.748331477 Simplifying s + 0.4 = -0.748331477 Reorder the terms: 0.4 + s = -0.748331477 Solving 0.4 + s = -0.748331477 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 = -0.748331477 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + s = -0.748331477 + -0.4 s = -0.748331477 + -0.4 Combine like terms: -0.748331477 + -0.4 = -1.148331477 s = -1.148331477 Simplifying s = -1.148331477

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.348331477, -1.148331477}

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