-7k(k-3)-(-8-3)=-3

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Solution for -7k(k-3)-(-8-3)=-3 equation:


Simplifying
-7k(k + -3) + -1(-8 + -3) = -3

Reorder the terms:
-7k(-3 + k) + -1(-8 + -3) = -3
(-3 * -7k + k * -7k) + -1(-8 + -3) = -3
(21k + -7k2) + -1(-8 + -3) = -3

Combine like terms: -8 + -3 = -11
21k + -7k2 + -1(-11) = -3

Multiply -1 * -11
21k + -7k2 + 11 = -3

Reorder the terms:
11 + 21k + -7k2 = -3

Solving
11 + 21k + -7k2 = -3

Solving for variable 'k'.

Reorder the terms:
11 + 3 + 21k + -7k2 = -3 + 3

Combine like terms: 11 + 3 = 14
14 + 21k + -7k2 = -3 + 3

Combine like terms: -3 + 3 = 0
14 + 21k + -7k2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(2 + 3k + -1k2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(2 + 3k + -1k2)' equal to zero and attempt to solve:

Simplifying
2 + 3k + -1k2 = 0

Solving
2 + 3k + -1k2 = 0

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

Divide each side by '-1'.
-2 + -3k + k2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + -3k + k2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3k + k2 = 0 + 2
-3k + k2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3k + k2 = 2

The k term is -3k.  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.
-3k + 2.25 + k2 = 2 + 2.25

Reorder the terms:
2.25 + -3k + k2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3k + k2 = 4.25

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

Calculate the square root of the right side: 2.061552813

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


Subproblem 1
k + -1.5 = 2.061552813

Simplifying
k + -1.5 = 2.061552813

Reorder the terms:
-1.5 + k = 2.061552813

Solving
-1.5 + k = 2.061552813

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = 2.061552813 + 1.5
k = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
k = 3.561552813

Simplifying
k = 3.561552813


Subproblem 2
k + -1.5 = -2.061552813

Simplifying
k + -1.5 = -2.061552813

Reorder the terms:
-1.5 + k = -2.061552813

Solving
-1.5 + k = -2.061552813

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = -2.061552813 + 1.5
k = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
k = -0.561552813

Simplifying
k = -0.561552813


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

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