k^2+6k-5=0

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Solution for k^2+6k-5=0 equation:


Simplifying
k2 + 6k + -5 = 0

Reorder the terms:
-5 + 6k + k2 = 0

Solving
-5 + 6k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6k + 5 + k2 = 0 + 5

Reorder the terms:
-5 + 5 + 6k + k2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6k + k2 = 0 + 5
6k + k2 = 0 + 5

Combine like terms: 0 + 5 = 5
6k + k2 = 5

The k term is 6k.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6k + 9 + k2 = 5 + 9

Reorder the terms:
9 + 6k + k2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6k + k2 = 14

Factor a perfect square on the left side:
(k + 3)(k + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(k + 3) equal to 3.741657387 and -3.741657387.

Subproblem 1

k + 3 = 3.741657387 Simplifying k + 3 = 3.741657387 Reorder the terms: 3 + k = 3.741657387 Solving 3 + k = 3.741657387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + k = 3.741657387 + -3 k = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 k = 0.741657387 Simplifying k = 0.741657387

Subproblem 2

k + 3 = -3.741657387 Simplifying k + 3 = -3.741657387 Reorder the terms: 3 + k = -3.741657387 Solving 3 + k = -3.741657387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + k = -3.741657387 + -3 k = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 k = -6.741657387 Simplifying k = -6.741657387

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.741657387, -6.741657387}

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