s^2+6s=8+0

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Solution for s^2+6s=8+0 equation:


Simplifying
s2 + 6s = 8 + 0

Reorder the terms:
6s + s2 = 8 + 0

Combine like terms: 8 + 0 = 8
6s + s2 = 8

Solving
6s + s2 = 8

Solving for variable 's'.

Reorder the terms:
-8 + 6s + s2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 6s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 6s + 8 + s2 = 0 + 8

Reorder the terms:
-8 + 8 + 6s + s2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 6s + s2 = 0 + 8
6s + s2 = 0 + 8

Combine like terms: 0 + 8 = 8
6s + s2 = 8

The s term is 6s.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6s + 9 + s2 = 8 + 9

Reorder the terms:
9 + 6s + s2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + 6s + s2 = 17

Factor a perfect square on the left side:
(s + 3)(s + 3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(s + 3) equal to 4.123105626 and -4.123105626.

Subproblem 1

s + 3 = 4.123105626 Simplifying s + 3 = 4.123105626 Reorder the terms: 3 + s = 4.123105626 Solving 3 + s = 4.123105626 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + s = 4.123105626 + -3 s = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 s = 1.123105626 Simplifying s = 1.123105626

Subproblem 2

s + 3 = -4.123105626 Simplifying s + 3 = -4.123105626 Reorder the terms: 3 + s = -4.123105626 Solving 3 + s = -4.123105626 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + s = -4.123105626 + -3 s = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 s = -7.123105626 Simplifying s = -7.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. s = {1.123105626, -7.123105626}

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