5k^2-13+9k-2k^2-15k=

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Solution for 5k^2-13+9k-2k^2-15k= equation:


Simplifying
5k2 + -13 + 9k + -2k2 + -15k = 0

Reorder the terms:
-13 + 9k + -15k + 5k2 + -2k2 = 0

Combine like terms: 9k + -15k = -6k
-13 + -6k + 5k2 + -2k2 = 0

Combine like terms: 5k2 + -2k2 = 3k2
-13 + -6k + 3k2 = 0

Solving
-13 + -6k + 3k2 = 0

Solving for variable 'k'.

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

Divide each side by '3'.
-4.333333333 + -2k + k2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + -2k + 4.333333333 + k2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + -2k + k2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + -2k + k2 = 0 + 4.333333333
-2k + k2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
-2k + k2 = 4.333333333

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = 4.333333333 + 1

Reorder the terms:
1 + -2k + k2 = 4.333333333 + 1

Combine like terms: 4.333333333 + 1 = 5.333333333
1 + -2k + k2 = 5.333333333

Factor a perfect square on the left side:
(k + -1)(k + -1) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(k + -1) equal to 2.309401077 and -2.309401077.

Subproblem 1

k + -1 = 2.309401077 Simplifying k + -1 = 2.309401077 Reorder the terms: -1 + k = 2.309401077 Solving -1 + k = 2.309401077 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = 2.309401077 + 1 Combine like terms: -1 + 1 = 0 0 + k = 2.309401077 + 1 k = 2.309401077 + 1 Combine like terms: 2.309401077 + 1 = 3.309401077 k = 3.309401077 Simplifying k = 3.309401077

Subproblem 2

k + -1 = -2.309401077 Simplifying k + -1 = -2.309401077 Reorder the terms: -1 + k = -2.309401077 Solving -1 + k = -2.309401077 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = -2.309401077 + 1 Combine like terms: -1 + 1 = 0 0 + k = -2.309401077 + 1 k = -2.309401077 + 1 Combine like terms: -2.309401077 + 1 = -1.309401077 k = -1.309401077 Simplifying k = -1.309401077

Solution

The solution to the problem is based on the solutions from the subproblems. k = {3.309401077, -1.309401077}

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