s^2-3s-2=0

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Solution for s^2-3s-2=0 equation:


Simplifying
s2 + -3s + -2 = 0

Reorder the terms:
-2 + -3s + s2 = 0

Solving
-2 + -3s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3s + 2 + s2 = 0 + 2

Reorder the terms:
-2 + 2 + -3s + s2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3s + s2 = 0 + 2
-3s + s2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3s + s2 = 2

The s term is -3s.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3s + 2.25 + s2 = 2 + 2.25

Reorder the terms:
2.25 + -3s + s2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3s + s2 = 4.25

Factor a perfect square on the left side:
(s + -1.5)(s + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(s + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

s + -1.5 = 2.061552813 Simplifying s + -1.5 = 2.061552813 Reorder the terms: -1.5 + s = 2.061552813 Solving -1.5 + s = 2.061552813 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + s = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + s = 2.061552813 + 1.5 s = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 s = 3.561552813 Simplifying s = 3.561552813

Subproblem 2

s + -1.5 = -2.061552813 Simplifying s + -1.5 = -2.061552813 Reorder the terms: -1.5 + s = -2.061552813 Solving -1.5 + s = -2.061552813 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + s = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + s = -2.061552813 + 1.5 s = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 s = -0.561552813 Simplifying s = -0.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. s = {3.561552813, -0.561552813}

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