k^2-(4*1*(-k+1))=7

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


Simplifying
k2 + -1(4 * 1(-1k + 1)) = 7

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

Multiply 4 * 1
k2 + -1(4(1 + -1k)) = 7
k2 + -1((1 * 4 + -1k * 4)) = 7
k2 + -1((4 + -4k)) = 7
k2 + (4 * -1 + -4k * -1) = 7
k2 + (-4 + 4k) = 7

Reorder the terms:
-4 + 4k + k2 = 7

Solving
-4 + 4k + k2 = 7

Solving for variable 'k'.

Reorder the terms:
-4 + -7 + 4k + k2 = 7 + -7

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

Combine like terms: 7 + -7 = 0
-11 + 4k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 4k + 11 + k2 = 0 + 11

Reorder the terms:
-11 + 11 + 4k + k2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4k + k2 = 0 + 11
4k + k2 = 0 + 11

Combine like terms: 0 + 11 = 11
4k + k2 = 11

The k term is 4k.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4k + 4 + k2 = 11 + 4

Reorder the terms:
4 + 4k + k2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + 4k + k2 = 15

Factor a perfect square on the left side:
(k + 2)(k + 2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(k + 2) equal to 3.872983346 and -3.872983346.


Subproblem 1
k + 2 = 3.872983346

Simplifying
k + 2 = 3.872983346

Reorder the terms:
2 + k = 3.872983346

Solving
2 + k = 3.872983346

Solving for variable 'k'.

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

Add '-2' to each side of the equation.
2 + -2 + k = 3.872983346 + -2

Combine like terms: 2 + -2 = 0
0 + k = 3.872983346 + -2
k = 3.872983346 + -2

Combine like terms: 3.872983346 + -2 = 1.872983346
k = 1.872983346

Simplifying
k = 1.872983346


Subproblem 2
k + 2 = -3.872983346

Simplifying
k + 2 = -3.872983346

Reorder the terms:
2 + k = -3.872983346

Solving
2 + k = -3.872983346

Solving for variable 'k'.

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

Add '-2' to each side of the equation.
2 + -2 + k = -3.872983346 + -2

Combine like terms: 2 + -2 = 0
0 + k = -3.872983346 + -2
k = -3.872983346 + -2

Combine like terms: -3.872983346 + -2 = -5.872983346
k = -5.872983346

Simplifying
k = -5.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.872983346, -5.872983346}

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