7s^2=-13-28s

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Solution for 7s^2=-13-28s equation:


Simplifying
7s2 = -13 + -28s

Solving
7s2 = -13 + -28s

Solving for variable 's'.

Reorder the terms:
13 + 28s + 7s2 = -13 + -28s + 13 + 28s

Reorder the terms:
13 + 28s + 7s2 = -13 + 13 + -28s + 28s

Combine like terms: -13 + 13 = 0
13 + 28s + 7s2 = 0 + -28s + 28s
13 + 28s + 7s2 = -28s + 28s

Combine like terms: -28s + 28s = 0
13 + 28s + 7s2 = 0

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

Divide each side by '7'.
1.857142857 + 4s + s2 = 0

Move the constant term to the right:

Add '-1.857142857' to each side of the equation.
1.857142857 + 4s + -1.857142857 + s2 = 0 + -1.857142857

Reorder the terms:
1.857142857 + -1.857142857 + 4s + s2 = 0 + -1.857142857

Combine like terms: 1.857142857 + -1.857142857 = 0.000000000
0.000000000 + 4s + s2 = 0 + -1.857142857
4s + s2 = 0 + -1.857142857

Combine like terms: 0 + -1.857142857 = -1.857142857
4s + s2 = -1.857142857

The s term is 4s.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4s + 4 + s2 = -1.857142857 + 4

Reorder the terms:
4 + 4s + s2 = -1.857142857 + 4

Combine like terms: -1.857142857 + 4 = 2.142857143
4 + 4s + s2 = 2.142857143

Factor a perfect square on the left side:
(s + 2)(s + 2) = 2.142857143

Calculate the square root of the right side: 1.463850109

Break this problem into two subproblems by setting 
(s + 2) equal to 1.463850109 and -1.463850109.

Subproblem 1

s + 2 = 1.463850109 Simplifying s + 2 = 1.463850109 Reorder the terms: 2 + s = 1.463850109 Solving 2 + s = 1.463850109 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 1.463850109 + -2 Combine like terms: 2 + -2 = 0 0 + s = 1.463850109 + -2 s = 1.463850109 + -2 Combine like terms: 1.463850109 + -2 = -0.536149891 s = -0.536149891 Simplifying s = -0.536149891

Subproblem 2

s + 2 = -1.463850109 Simplifying s + 2 = -1.463850109 Reorder the terms: 2 + s = -1.463850109 Solving 2 + s = -1.463850109 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -1.463850109 + -2 Combine like terms: 2 + -2 = 0 0 + s = -1.463850109 + -2 s = -1.463850109 + -2 Combine like terms: -1.463850109 + -2 = -3.463850109 s = -3.463850109 Simplifying s = -3.463850109

Solution

The solution to the problem is based on the solutions from the subproblems. s = {-0.536149891, -3.463850109}

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