2k-1=(k^2-7)-3k-4

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Solution for 2k-1=(k^2-7)-3k-4 equation:


Simplifying
2k + -1 = (k2 + -7) + -3k + -4

Reorder the terms:
-1 + 2k = (k2 + -7) + -3k + -4

Reorder the terms:
-1 + 2k = (-7 + k2) + -3k + -4

Remove parenthesis around (-7 + k2)
-1 + 2k = -7 + k2 + -3k + -4

Reorder the terms:
-1 + 2k = -7 + -4 + -3k + k2

Combine like terms: -7 + -4 = -11
-1 + 2k = -11 + -3k + k2

Solving
-1 + 2k = -11 + -3k + k2

Solving for variable 'k'.

Reorder the terms:
-1 + 11 + 2k + 3k + -1k2 = -11 + -3k + k2 + 11 + 3k + -1k2

Combine like terms: -1 + 11 = 10
10 + 2k + 3k + -1k2 = -11 + -3k + k2 + 11 + 3k + -1k2

Combine like terms: 2k + 3k = 5k
10 + 5k + -1k2 = -11 + -3k + k2 + 11 + 3k + -1k2

Reorder the terms:
10 + 5k + -1k2 = -11 + 11 + -3k + 3k + k2 + -1k2

Combine like terms: -11 + 11 = 0
10 + 5k + -1k2 = 0 + -3k + 3k + k2 + -1k2
10 + 5k + -1k2 = -3k + 3k + k2 + -1k2

Combine like terms: -3k + 3k = 0
10 + 5k + -1k2 = 0 + k2 + -1k2
10 + 5k + -1k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
10 + 5k + -1k2 = 0

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

Divide each side by '-1'.
-10 + -5k + k2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -5k + 10 + k2 = 0 + 10

Reorder the terms:
-10 + 10 + -5k + k2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -5k + k2 = 0 + 10
-5k + k2 = 0 + 10

Combine like terms: 0 + 10 = 10
-5k + k2 = 10

The k term is -5k.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5k + 6.25 + k2 = 10 + 6.25

Reorder the terms:
6.25 + -5k + k2 = 10 + 6.25

Combine like terms: 10 + 6.25 = 16.25
6.25 + -5k + k2 = 16.25

Factor a perfect square on the left side:
(k + -2.5)(k + -2.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(k + -2.5) equal to 4.031128874 and -4.031128874.

Subproblem 1

k + -2.5 = 4.031128874 Simplifying k + -2.5 = 4.031128874 Reorder the terms: -2.5 + k = 4.031128874 Solving -2.5 + k = 4.031128874 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + k = 4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + k = 4.031128874 + 2.5 k = 4.031128874 + 2.5 Combine like terms: 4.031128874 + 2.5 = 6.531128874 k = 6.531128874 Simplifying k = 6.531128874

Subproblem 2

k + -2.5 = -4.031128874 Simplifying k + -2.5 = -4.031128874 Reorder the terms: -2.5 + k = -4.031128874 Solving -2.5 + k = -4.031128874 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + k = -4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + k = -4.031128874 + 2.5 k = -4.031128874 + 2.5 Combine like terms: -4.031128874 + 2.5 = -1.531128874 k = -1.531128874 Simplifying k = -1.531128874

Solution

The solution to the problem is based on the solutions from the subproblems. k = {6.531128874, -1.531128874}

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