s^2-s-5=

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


Simplifying
s2 + -1s + -5 = 0

Reorder the terms:
-5 + -1s + s2 = 0

Solving
-5 + -1s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -1s + 5 + s2 = 0 + 5

Reorder the terms:
-5 + 5 + -1s + s2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1s + s2 = 0 + 5
-1s + s2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1s + s2 = 5

The s term is -1s.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1s + 0.25 + s2 = 5 + 0.25

Reorder the terms:
0.25 + -1s + s2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + -1s + s2 = 5.25

Factor a perfect square on the left side:
(s + -0.5)(s + -0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(s + -0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

s + -0.5 = 2.291287847 Simplifying s + -0.5 = 2.291287847 Reorder the terms: -0.5 + s = 2.291287847 Solving -0.5 + s = 2.291287847 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = 2.291287847 + 0.5 s = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 s = 2.791287847 Simplifying s = 2.791287847

Subproblem 2

s + -0.5 = -2.291287847 Simplifying s + -0.5 = -2.291287847 Reorder the terms: -0.5 + s = -2.291287847 Solving -0.5 + s = -2.291287847 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = -2.291287847 + 0.5 s = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 s = -1.791287847 Simplifying s = -1.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. s = {2.791287847, -1.791287847}

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