4k^2+84k+252=0

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Solution for 4k^2+84k+252=0 equation: 


Simplifying
4k2 + 84k + 252 = 0

Reorder the terms:
252 + 84k + 4k2 = 0

Solving
252 + 84k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(63 + 21k + k2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(63 + 21k + k2)' equal to zero and attempt to solve:

Simplifying
63 + 21k + k2 = 0

Solving
63 + 21k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-63' to each side of the equation.
63 + 21k + -63 + k2 = 0 + -63

Reorder the terms:
63 + -63 + 21k + k2 = 0 + -63

Combine like terms: 63 + -63 = 0
0 + 21k + k2 = 0 + -63
21k + k2 = 0 + -63

Combine like terms: 0 + -63 = -63
21k + k2 = -63

The k term is 21k.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21k + 110.25 + k2 = -63 + 110.25

Reorder the terms:
110.25 + 21k + k2 = -63 + 110.25

Combine like terms: -63 + 110.25 = 47.25
110.25 + 21k + k2 = 47.25

Factor a perfect square on the left side:
(k + 10.5)(k + 10.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(k + 10.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
k + 10.5 = 6.873863542

Simplifying
k + 10.5 = 6.873863542

Reorder the terms:
10.5 + k = 6.873863542

Solving
10.5 + k = 6.873863542

Solving for variable 'k'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + k = 6.873863542 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + k = 6.873863542 + -10.5
k = 6.873863542 + -10.5

Combine like terms: 6.873863542 + -10.5 = -3.626136458
k = -3.626136458

Simplifying
k = -3.626136458


Subproblem 2
k + 10.5 = -6.873863542

Simplifying
k + 10.5 = -6.873863542

Reorder the terms:
10.5 + k = -6.873863542

Solving
10.5 + k = -6.873863542

Solving for variable 'k'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + k = -6.873863542 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + k = -6.873863542 + -10.5
k = -6.873863542 + -10.5

Combine like terms: -6.873863542 + -10.5 = -17.373863542
k = -17.373863542

Simplifying
k = -17.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-3.626136458, -17.373863542}
Solution
k = {-3.626136458, -17.373863542}

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