s^2+15s-375=0

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Solution for s^2+15s-375=0 equation:


Simplifying
s2 + 15s + -375 = 0

Reorder the terms:
-375 + 15s + s2 = 0

Solving
-375 + 15s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '375' to each side of the equation.
-375 + 15s + 375 + s2 = 0 + 375

Reorder the terms:
-375 + 375 + 15s + s2 = 0 + 375

Combine like terms: -375 + 375 = 0
0 + 15s + s2 = 0 + 375
15s + s2 = 0 + 375

Combine like terms: 0 + 375 = 375
15s + s2 = 375

The s term is 15s.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15s + 56.25 + s2 = 375 + 56.25

Reorder the terms:
56.25 + 15s + s2 = 375 + 56.25

Combine like terms: 375 + 56.25 = 431.25
56.25 + 15s + s2 = 431.25

Factor a perfect square on the left side:
(s + 7.5)(s + 7.5) = 431.25

Calculate the square root of the right side: 20.766559657

Break this problem into two subproblems by setting 
(s + 7.5) equal to 20.766559657 and -20.766559657.

Subproblem 1

s + 7.5 = 20.766559657 Simplifying s + 7.5 = 20.766559657 Reorder the terms: 7.5 + s = 20.766559657 Solving 7.5 + s = 20.766559657 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + s = 20.766559657 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + s = 20.766559657 + -7.5 s = 20.766559657 + -7.5 Combine like terms: 20.766559657 + -7.5 = 13.266559657 s = 13.266559657 Simplifying s = 13.266559657

Subproblem 2

s + 7.5 = -20.766559657 Simplifying s + 7.5 = -20.766559657 Reorder the terms: 7.5 + s = -20.766559657 Solving 7.5 + s = -20.766559657 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + s = -20.766559657 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + s = -20.766559657 + -7.5 s = -20.766559657 + -7.5 Combine like terms: -20.766559657 + -7.5 = -28.266559657 s = -28.266559657 Simplifying s = -28.266559657

Solution

The solution to the problem is based on the solutions from the subproblems. s = {13.266559657, -28.266559657}

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