7k^2+20k-12=0

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Solution for 7k^2+20k-12=0 equation:


Simplifying
7k2 + 20k + -12 = 0

Reorder the terms:
-12 + 20k + 7k2 = 0

Solving
-12 + 20k + 7k2 = 0

Solving for variable 'k'.

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

Divide each side by '7'.
-1.714285714 + 2.857142857k + k2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + 2.857142857k + 1.714285714 + k2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + 2.857142857k + k2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + 2.857142857k + k2 = 0 + 1.714285714
2.857142857k + k2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
2.857142857k + k2 = 1.714285714

The k term is 2.857142857k.  Take half its coefficient (1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
2.857142857k + 2.040816328 + k2 = 1.714285714 + 2.040816328

Reorder the terms:
2.040816328 + 2.857142857k + k2 = 1.714285714 + 2.040816328

Combine like terms: 1.714285714 + 2.040816328 = 3.755102042
2.040816328 + 2.857142857k + k2 = 3.755102042

Factor a perfect square on the left side:
(k + 1.428571429)(k + 1.428571429) = 3.755102042

Calculate the square root of the right side: 1.937808567

Break this problem into two subproblems by setting 
(k + 1.428571429) equal to 1.937808567 and -1.937808567.

Subproblem 1

k + 1.428571429 = 1.937808567 Simplifying k + 1.428571429 = 1.937808567 Reorder the terms: 1.428571429 + k = 1.937808567 Solving 1.428571429 + k = 1.937808567 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + k = 1.937808567 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + k = 1.937808567 + -1.428571429 k = 1.937808567 + -1.428571429 Combine like terms: 1.937808567 + -1.428571429 = 0.509237138 k = 0.509237138 Simplifying k = 0.509237138

Subproblem 2

k + 1.428571429 = -1.937808567 Simplifying k + 1.428571429 = -1.937808567 Reorder the terms: 1.428571429 + k = -1.937808567 Solving 1.428571429 + k = -1.937808567 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + k = -1.937808567 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + k = -1.937808567 + -1.428571429 k = -1.937808567 + -1.428571429 Combine like terms: -1.937808567 + -1.428571429 = -3.366379996 k = -3.366379996 Simplifying k = -3.366379996

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.509237138, -3.366379996}

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