s^2+5s=-8

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Solution for s^2+5s=-8 equation:


Simplifying
s2 + 5s = -8

Reorder the terms:
5s + s2 = -8

Solving
5s + s2 = -8

Solving for variable 's'.

Reorder the terms:
8 + 5s + s2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 5s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 5s + -8 + s2 = 0 + -8

Reorder the terms:
8 + -8 + 5s + s2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5s + s2 = 0 + -8
5s + s2 = 0 + -8

Combine like terms: 0 + -8 = -8
5s + s2 = -8

The s term is 5s.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5s + 6.25 + s2 = -8 + 6.25

Reorder the terms:
6.25 + 5s + s2 = -8 + 6.25

Combine like terms: -8 + 6.25 = -1.75
6.25 + 5s + s2 = -1.75

Factor a perfect square on the left side:
(s + 2.5)(s + 2.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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