K^2+4K-70=0

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Solution for K^2+4K-70=0 equation: 


Simplifying
K2 + 4K + -70 = 0

Reorder the terms:
-70 + 4K + K2 = 0

Solving
-70 + 4K + K2 = 0

Solving for variable 'K'.

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 4K + 70 + K2 = 0 + 70

Reorder the terms:
-70 + 70 + 4K + K2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 4K + K2 = 0 + 70
4K + K2 = 0 + 70

Combine like terms: 0 + 70 = 70
4K + K2 = 70

The K term is 4K.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4K + 4 + K2 = 70 + 4

Reorder the terms:
4 + 4K + K2 = 70 + 4

Combine like terms: 70 + 4 = 74
4 + 4K + K2 = 74

Factor a perfect square on the left side:
(K + 2)(K + 2) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(K + 2) equal to 8.602325267 and -8.602325267.


Subproblem 1
K + 2 = 8.602325267

Simplifying
K + 2 = 8.602325267

Reorder the terms:
2 + K = 8.602325267

Solving
2 + K = 8.602325267

Solving for variable 'K'.

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

Add '-2' to each side of the equation.
2 + -2 + K = 8.602325267 + -2

Combine like terms: 2 + -2 = 0
0 + K = 8.602325267 + -2
K = 8.602325267 + -2

Combine like terms: 8.602325267 + -2 = 6.602325267
K = 6.602325267

Simplifying
K = 6.602325267


Subproblem 2
K + 2 = -8.602325267

Simplifying
K + 2 = -8.602325267

Reorder the terms:
2 + K = -8.602325267

Solving
2 + K = -8.602325267

Solving for variable 'K'.

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

Add '-2' to each side of the equation.
2 + -2 + K = -8.602325267 + -2

Combine like terms: 2 + -2 = 0
0 + K = -8.602325267 + -2
K = -8.602325267 + -2

Combine like terms: -8.602325267 + -2 = -10.602325267
K = -10.602325267

Simplifying
K = -10.602325267


Solution
The solution to the problem is based on the solutions
from the subproblems.
K = {6.602325267, -10.602325267}

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