6s^2+9s-5=0

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Solution for 6s^2+9s-5=0 equation:


Simplifying
6s2 + 9s + -5 = 0

Reorder the terms:
-5 + 9s + 6s2 = 0

Solving
-5 + 9s + 6s2 = 0

Solving for variable 's'.

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

Divide each side by '6'.
-0.8333333333 + 1.5s + s2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 1.5s + 0.8333333333 + s2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 1.5s + s2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 1.5s + s2 = 0 + 0.8333333333
1.5s + s2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
1.5s + s2 = 0.8333333333

The s term is 1.5s.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5s + 0.5625 + s2 = 0.8333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5s + s2 = 0.8333333333 + 0.5625

Combine like terms: 0.8333333333 + 0.5625 = 1.3958333333
0.5625 + 1.5s + s2 = 1.3958333333

Factor a perfect square on the left side:
(s + 0.75)(s + 0.75) = 1.3958333333

Calculate the square root of the right side: 1.181453907

Break this problem into two subproblems by setting 
(s + 0.75) equal to 1.181453907 and -1.181453907.

Subproblem 1

s + 0.75 = 1.181453907 Simplifying s + 0.75 = 1.181453907 Reorder the terms: 0.75 + s = 1.181453907 Solving 0.75 + s = 1.181453907 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = 1.181453907 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = 1.181453907 + -0.75 s = 1.181453907 + -0.75 Combine like terms: 1.181453907 + -0.75 = 0.431453907 s = 0.431453907 Simplifying s = 0.431453907

Subproblem 2

s + 0.75 = -1.181453907 Simplifying s + 0.75 = -1.181453907 Reorder the terms: 0.75 + s = -1.181453907 Solving 0.75 + s = -1.181453907 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = -1.181453907 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = -1.181453907 + -0.75 s = -1.181453907 + -0.75 Combine like terms: -1.181453907 + -0.75 = -1.931453907 s = -1.931453907 Simplifying s = -1.931453907

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.431453907, -1.931453907}

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