s^2-24s-37=0

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Solution for s^2-24s-37=0 equation:


Simplifying
s2 + -24s + -37 = 0

Reorder the terms:
-37 + -24s + s2 = 0

Solving
-37 + -24s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -24s + 37 + s2 = 0 + 37

Reorder the terms:
-37 + 37 + -24s + s2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -24s + s2 = 0 + 37
-24s + s2 = 0 + 37

Combine like terms: 0 + 37 = 37
-24s + s2 = 37

The s term is -24s.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24s + 144 + s2 = 37 + 144

Reorder the terms:
144 + -24s + s2 = 37 + 144

Combine like terms: 37 + 144 = 181
144 + -24s + s2 = 181

Factor a perfect square on the left side:
(s + -12)(s + -12) = 181

Calculate the square root of the right side: 13.453624047

Break this problem into two subproblems by setting 
(s + -12) equal to 13.453624047 and -13.453624047.

Subproblem 1

s + -12 = 13.453624047 Simplifying s + -12 = 13.453624047 Reorder the terms: -12 + s = 13.453624047 Solving -12 + s = 13.453624047 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + s = 13.453624047 + 12 Combine like terms: -12 + 12 = 0 0 + s = 13.453624047 + 12 s = 13.453624047 + 12 Combine like terms: 13.453624047 + 12 = 25.453624047 s = 25.453624047 Simplifying s = 25.453624047

Subproblem 2

s + -12 = -13.453624047 Simplifying s + -12 = -13.453624047 Reorder the terms: -12 + s = -13.453624047 Solving -12 + s = -13.453624047 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + s = -13.453624047 + 12 Combine like terms: -12 + 12 = 0 0 + s = -13.453624047 + 12 s = -13.453624047 + 12 Combine like terms: -13.453624047 + 12 = -1.453624047 s = -1.453624047 Simplifying s = -1.453624047

Solution

The solution to the problem is based on the solutions from the subproblems. s = {25.453624047, -1.453624047}

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