6k^2+12k-15=10

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Solution for 6k^2+12k-15=10 equation:


Simplifying
6k2 + 12k + -15 = 10

Reorder the terms:
-15 + 12k + 6k2 = 10

Solving
-15 + 12k + 6k2 = 10

Solving for variable 'k'.

Reorder the terms:
-15 + -10 + 12k + 6k2 = 10 + -10

Combine like terms: -15 + -10 = -25
-25 + 12k + 6k2 = 10 + -10

Combine like terms: 10 + -10 = 0
-25 + 12k + 6k2 = 0

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

Divide each side by '6'.
-4.166666667 + 2k + k2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 2k + 4.166666667 + k2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 2k + k2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 2k + k2 = 0 + 4.166666667
2k + k2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
2k + k2 = 4.166666667

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 = 4.166666667 + 1

Reorder the terms:
1 + 2k + k2 = 4.166666667 + 1

Combine like terms: 4.166666667 + 1 = 5.166666667
1 + 2k + k2 = 5.166666667

Factor a perfect square on the left side:
(k + 1)(k + 1) = 5.166666667

Calculate the square root of the right side: 2.273030283

Break this problem into two subproblems by setting 
(k + 1) equal to 2.273030283 and -2.273030283.

Subproblem 1

k + 1 = 2.273030283 Simplifying k + 1 = 2.273030283 Reorder the terms: 1 + k = 2.273030283 Solving 1 + k = 2.273030283 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 = 2.273030283 + -1 Combine like terms: 1 + -1 = 0 0 + k = 2.273030283 + -1 k = 2.273030283 + -1 Combine like terms: 2.273030283 + -1 = 1.273030283 k = 1.273030283 Simplifying k = 1.273030283

Subproblem 2

k + 1 = -2.273030283 Simplifying k + 1 = -2.273030283 Reorder the terms: 1 + k = -2.273030283 Solving 1 + k = -2.273030283 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 = -2.273030283 + -1 Combine like terms: 1 + -1 = 0 0 + k = -2.273030283 + -1 k = -2.273030283 + -1 Combine like terms: -2.273030283 + -1 = -3.273030283 k = -3.273030283 Simplifying k = -3.273030283

Solution

The solution to the problem is based on the solutions from the subproblems. k = {1.273030283, -3.273030283}

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