4k^2-2k-15=-5

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Solution for 4k^2-2k-15=-5 equation:


Simplifying
4k2 + -2k + -15 = -5

Reorder the terms:
-15 + -2k + 4k2 = -5

Solving
-15 + -2k + 4k2 = -5

Solving for variable 'k'.

Reorder the terms:
-15 + 5 + -2k + 4k2 = -5 + 5

Combine like terms: -15 + 5 = -10
-10 + -2k + 4k2 = -5 + 5

Combine like terms: -5 + 5 = 0
-10 + -2k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -1k + 2k2) = 0

Ignore the factor 2.

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

Simplifying
-5 + -1k + 2k2 = 0

Solving
-5 + -1k + 2k2 = 0

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

Divide each side by '2'.
-2.5 + -0.5k + k2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.5k + 2.5 + k2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.5k + k2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.5k + k2 = 0 + 2.5
-0.5k + k2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.5k + k2 = 2.5

The k term is -0.5k.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5k + 0.0625 + k2 = 2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5k + k2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + -0.5k + k2 = 2.5625

Factor a perfect square on the left side:
(k + -0.25)(k + -0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(k + -0.25) equal to 1.600781059 and -1.600781059.


Subproblem 1
k + -0.25 = 1.600781059

Simplifying
k + -0.25 = 1.600781059

Reorder the terms:
-0.25 + k = 1.600781059

Solving
-0.25 + k = 1.600781059

Solving for variable 'k'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + k = 1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + k = 1.600781059 + 0.25
k = 1.600781059 + 0.25

Combine like terms: 1.600781059 + 0.25 = 1.850781059
k = 1.850781059

Simplifying
k = 1.850781059


Subproblem 2
k + -0.25 = -1.600781059

Simplifying
k + -0.25 = -1.600781059

Reorder the terms:
-0.25 + k = -1.600781059

Solving
-0.25 + k = -1.600781059

Solving for variable 'k'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + k = -1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + k = -1.600781059 + 0.25
k = -1.600781059 + 0.25

Combine like terms: -1.600781059 + 0.25 = -1.350781059
k = -1.350781059

Simplifying
k = -1.350781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.850781059, -1.350781059}
Solution
k = {1.850781059, -1.350781059}

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