4k^2+1806k-70526=0

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Solution for 4k^2+1806k-70526=0 equation: 


Simplifying
4k2 + 1806k + -70526 = 0

Reorder the terms:
-70526 + 1806k + 4k2 = 0

Solving
-70526 + 1806k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35263 + 903k + 2k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35263 + 903k + 2k2)' equal to zero and attempt to solve:

Simplifying
-35263 + 903k + 2k2 = 0

Solving
-35263 + 903k + 2k2 = 0

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

Divide each side by '2'.
-17631.5 + 451.5k + k2 = 0

Move the constant term to the right:

Add '17631.5' to each side of the equation.
-17631.5 + 451.5k + 17631.5 + k2 = 0 + 17631.5

Reorder the terms:
-17631.5 + 17631.5 + 451.5k + k2 = 0 + 17631.5

Combine like terms: -17631.5 + 17631.5 = 0.0
0.0 + 451.5k + k2 = 0 + 17631.5
451.5k + k2 = 0 + 17631.5

Combine like terms: 0 + 17631.5 = 17631.5
451.5k + k2 = 17631.5

The k term is 451.5k.  Take half its coefficient (225.75).
Square it (50963.0625) and add it to both sides.

Add '50963.0625' to each side of the equation.
451.5k + 50963.0625 + k2 = 17631.5 + 50963.0625

Reorder the terms:
50963.0625 + 451.5k + k2 = 17631.5 + 50963.0625

Combine like terms: 17631.5 + 50963.0625 = 68594.5625
50963.0625 + 451.5k + k2 = 68594.5625

Factor a perfect square on the left side:
(k + 225.75)(k + 225.75) = 68594.5625

Calculate the square root of the right side: 261.905636633

Break this problem into two subproblems by setting 
(k + 225.75) equal to 261.905636633 and -261.905636633.


Subproblem 1
k + 225.75 = 261.905636633

Simplifying
k + 225.75 = 261.905636633

Reorder the terms:
225.75 + k = 261.905636633

Solving
225.75 + k = 261.905636633

Solving for variable 'k'.

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

Add '-225.75' to each side of the equation.
225.75 + -225.75 + k = 261.905636633 + -225.75

Combine like terms: 225.75 + -225.75 = 0.00
0.00 + k = 261.905636633 + -225.75
k = 261.905636633 + -225.75

Combine like terms: 261.905636633 + -225.75 = 36.155636633
k = 36.155636633

Simplifying
k = 36.155636633


Subproblem 2
k + 225.75 = -261.905636633

Simplifying
k + 225.75 = -261.905636633

Reorder the terms:
225.75 + k = -261.905636633

Solving
225.75 + k = -261.905636633

Solving for variable 'k'.

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

Add '-225.75' to each side of the equation.
225.75 + -225.75 + k = -261.905636633 + -225.75

Combine like terms: 225.75 + -225.75 = 0.00
0.00 + k = -261.905636633 + -225.75
k = -261.905636633 + -225.75

Combine like terms: -261.905636633 + -225.75 = -487.655636633
k = -487.655636633

Simplifying
k = -487.655636633


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {36.155636633, -487.655636633}
Solution
k = {36.155636633, -487.655636633}

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