9s^2+42s-49=

Solution for 9s^2+42s-49= equation:

Simplifying
9s2 + 42s + -49 = 0

Reorder the terms:
-49 + 42s + 9s2 = 0

Solving
-49 + 42s + 9s2 = 0

Solving for variable 's'.

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

Divide each side by '9'.
-5.444444444 + 4.666666667s + s2 = 0

Move the constant term to the right:

Add '5.444444444' to each side of the equation.
-5.444444444 + 4.666666667s + 5.444444444 + s2 = 0 + 5.444444444

Reorder the terms:
-5.444444444 + 5.444444444 + 4.666666667s + s2 = 0 + 5.444444444

Combine like terms: -5.444444444 + 5.444444444 = 0.000000000
0.000000000 + 4.666666667s + s2 = 0 + 5.444444444
4.666666667s + s2 = 0 + 5.444444444

Combine like terms: 0 + 5.444444444 = 5.444444444
4.666666667s + s2 = 5.444444444

The s term is 4.666666667s.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667s + 5.444444448 + s2 = 5.444444444 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667s + s2 = 5.444444444 + 5.444444448

Combine like terms: 5.444444444 + 5.444444448 = 10.888888892
5.444444448 + 4.666666667s + s2 = 10.888888892

Factor a perfect square on the left side:
(s + 2.333333334)(s + 2.333333334) = 10.888888892

Calculate the square root of the right side: 3.299831646

Break this problem into two subproblems by setting 
(s + 2.333333334) equal to 3.299831646 and -3.299831646.

Subproblem 1
s + 2.333333334 = 3.299831646

Simplifying
s + 2.333333334 = 3.299831646

Reorder the terms:
2.333333334 + s = 3.299831646

Solving
2.333333334 + s = 3.299831646

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + s = 3.299831646 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + s = 3.299831646 + -2.333333334
s = 3.299831646 + -2.333333334

Combine like terms: 3.299831646 + -2.333333334 = 0.966498312
s = 0.966498312

Simplifying
s = 0.966498312

Subproblem 2
s + 2.333333334 = -3.299831646

Simplifying
s + 2.333333334 = -3.299831646

Reorder the terms:
2.333333334 + s = -3.299831646

Solving
2.333333334 + s = -3.299831646

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + s = -3.299831646 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + s = -3.299831646 + -2.333333334
s = -3.299831646 + -2.333333334

Combine like terms: -3.299831646 + -2.333333334 = -5.63316498
s = -5.63316498

Simplifying
s = -5.63316498

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.966498312, -5.63316498}