8s-11=(s-2)(s-4)

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Solution for 8s-11=(s-2)(s-4) equation:


Simplifying
8s + -11 = (s + -2)(s + -4)

Reorder the terms:
-11 + 8s = (s + -2)(s + -4)

Reorder the terms:
-11 + 8s = (-2 + s)(s + -4)

Reorder the terms:
-11 + 8s = (-2 + s)(-4 + s)

Multiply (-2 + s) * (-4 + s)
-11 + 8s = (-2(-4 + s) + s(-4 + s))
-11 + 8s = ((-4 * -2 + s * -2) + s(-4 + s))
-11 + 8s = ((8 + -2s) + s(-4 + s))
-11 + 8s = (8 + -2s + (-4 * s + s * s))
-11 + 8s = (8 + -2s + (-4s + s2))

Combine like terms: -2s + -4s = -6s
-11 + 8s = (8 + -6s + s2)

Solving
-11 + 8s = 8 + -6s + s2

Solving for variable 's'.

Reorder the terms:
-11 + -8 + 8s + 6s + -1s2 = 8 + -6s + s2 + -8 + 6s + -1s2

Combine like terms: -11 + -8 = -19
-19 + 8s + 6s + -1s2 = 8 + -6s + s2 + -8 + 6s + -1s2

Combine like terms: 8s + 6s = 14s
-19 + 14s + -1s2 = 8 + -6s + s2 + -8 + 6s + -1s2

Reorder the terms:
-19 + 14s + -1s2 = 8 + -8 + -6s + 6s + s2 + -1s2

Combine like terms: 8 + -8 = 0
-19 + 14s + -1s2 = 0 + -6s + 6s + s2 + -1s2
-19 + 14s + -1s2 = -6s + 6s + s2 + -1s2

Combine like terms: -6s + 6s = 0
-19 + 14s + -1s2 = 0 + s2 + -1s2
-19 + 14s + -1s2 = s2 + -1s2

Combine like terms: s2 + -1s2 = 0
-19 + 14s + -1s2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
19 + -14s + s2 = 0

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -14s + -19 + s2 = 0 + -19

Reorder the terms:
19 + -19 + -14s + s2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -14s + s2 = 0 + -19
-14s + s2 = 0 + -19

Combine like terms: 0 + -19 = -19
-14s + s2 = -19

The s term is -14s.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14s + 49 + s2 = -19 + 49

Reorder the terms:
49 + -14s + s2 = -19 + 49

Combine like terms: -19 + 49 = 30
49 + -14s + s2 = 30

Factor a perfect square on the left side:
(s + -7)(s + -7) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(s + -7) equal to 5.477225575 and -5.477225575.

Subproblem 1

s + -7 = 5.477225575 Simplifying s + -7 = 5.477225575 Reorder the terms: -7 + s = 5.477225575 Solving -7 + s = 5.477225575 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = 5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + s = 5.477225575 + 7 s = 5.477225575 + 7 Combine like terms: 5.477225575 + 7 = 12.477225575 s = 12.477225575 Simplifying s = 12.477225575

Subproblem 2

s + -7 = -5.477225575 Simplifying s + -7 = -5.477225575 Reorder the terms: -7 + s = -5.477225575 Solving -7 + s = -5.477225575 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = -5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + s = -5.477225575 + 7 s = -5.477225575 + 7 Combine like terms: -5.477225575 + 7 = 1.522774425 s = 1.522774425 Simplifying s = 1.522774425

Solution

The solution to the problem is based on the solutions from the subproblems. s = {12.477225575, 1.522774425}

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