7k^2+10k-100=2k^2+55

Solution for 7k^2+10k-100=2k^2+55 equation:

Simplifying
7k2 + 10k + -100 = 2k2 + 55

Reorder the terms:
-100 + 10k + 7k2 = 2k2 + 55

Reorder the terms:
-100 + 10k + 7k2 = 55 + 2k2

Solving
-100 + 10k + 7k2 = 55 + 2k2

Solving for variable 'k'.

Reorder the terms:
-100 + -55 + 10k + 7k2 + -2k2 = 55 + 2k2 + -55 + -2k2

Combine like terms: -100 + -55 = -155
-155 + 10k + 7k2 + -2k2 = 55 + 2k2 + -55 + -2k2

Combine like terms: 7k2 + -2k2 = 5k2
-155 + 10k + 5k2 = 55 + 2k2 + -55 + -2k2

Reorder the terms:
-155 + 10k + 5k2 = 55 + -55 + 2k2 + -2k2

Combine like terms: 55 + -55 = 0
-155 + 10k + 5k2 = 0 + 2k2 + -2k2
-155 + 10k + 5k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
-155 + 10k + 5k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-31 + 2k + k2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-31 + 2k + k2)' equal to zero and attempt to solve:

Simplifying
-31 + 2k + k2 = 0

Solving
-31 + 2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 2k + 31 + k2 = 0 + 31

Reorder the terms:
-31 + 31 + 2k + k2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 2k + k2 = 0 + 31
2k + k2 = 0 + 31

Combine like terms: 0 + 31 = 31
2k + k2 = 31

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = 31 + 1

Reorder the terms:
1 + 2k + k2 = 31 + 1

Combine like terms: 31 + 1 = 32
1 + 2k + k2 = 32

Factor a perfect square on the left side:
(k + 1)(k + 1) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(k + 1) equal to 5.656854249 and -5.656854249.

Subproblem 1
k + 1 = 5.656854249

Simplifying
k + 1 = 5.656854249

Reorder the terms:
1 + k = 5.656854249

Solving
1 + k = 5.656854249

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = 5.656854249 + -1

Combine like terms: 1 + -1 = 0
0 + k = 5.656854249 + -1
k = 5.656854249 + -1

Combine like terms: 5.656854249 + -1 = 4.656854249
k = 4.656854249

Simplifying
k = 4.656854249

Subproblem 2
k + 1 = -5.656854249

Simplifying
k + 1 = -5.656854249

Reorder the terms:
1 + k = -5.656854249

Solving
1 + k = -5.656854249

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = -5.656854249 + -1

Combine like terms: 1 + -1 = 0
0 + k = -5.656854249 + -1
k = -5.656854249 + -1

Combine like terms: -5.656854249 + -1 = -6.656854249
k = -6.656854249

Simplifying
k = -6.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.656854249, -6.656854249}
Solution
k = {4.656854249, -6.656854249}