2k^2+7k-2=0

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Solution for 2k^2+7k-2=0 equation: 


Simplifying
2k2 + 7k + -2 = 0

Reorder the terms:
-2 + 7k + 2k2 = 0

Solving
-2 + 7k + 2k2 = 0

Solving for variable 'k'.

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

Divide each side by '2'.
-1 + 3.5k + k2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3.5k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + 3.5k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3.5k + k2 = 0 + 1
3.5k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
3.5k + k2 = 1

The k term is 3.5k.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5k + 3.0625 + k2 = 1 + 3.0625

Reorder the terms:
3.0625 + 3.5k + k2 = 1 + 3.0625

Combine like terms: 1 + 3.0625 = 4.0625
3.0625 + 3.5k + k2 = 4.0625

Factor a perfect square on the left side:
(k + 1.75)(k + 1.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(k + 1.75) equal to 2.015564437 and -2.015564437.


Subproblem 1
k + 1.75 = 2.015564437

Simplifying
k + 1.75 = 2.015564437

Reorder the terms:
1.75 + k = 2.015564437

Solving
1.75 + k = 2.015564437

Solving for variable 'k'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + k = 2.015564437 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + k = 2.015564437 + -1.75
k = 2.015564437 + -1.75

Combine like terms: 2.015564437 + -1.75 = 0.265564437
k = 0.265564437

Simplifying
k = 0.265564437


Subproblem 2
k + 1.75 = -2.015564437

Simplifying
k + 1.75 = -2.015564437

Reorder the terms:
1.75 + k = -2.015564437

Solving
1.75 + k = -2.015564437

Solving for variable 'k'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + k = -2.015564437 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + k = -2.015564437 + -1.75
k = -2.015564437 + -1.75

Combine like terms: -2.015564437 + -1.75 = -3.765564437
k = -3.765564437

Simplifying
k = -3.765564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.265564437, -3.765564437}

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