5k^2=-12k+16

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Solution for 5k^2=-12k+16 equation:


Simplifying
5k2 = -12k + 16

Reorder the terms:
5k2 = 16 + -12k

Solving
5k2 = 16 + -12k

Solving for variable 'k'.

Reorder the terms:
-16 + 12k + 5k2 = 16 + -12k + -16 + 12k

Reorder the terms:
-16 + 12k + 5k2 = 16 + -16 + -12k + 12k

Combine like terms: 16 + -16 = 0
-16 + 12k + 5k2 = 0 + -12k + 12k
-16 + 12k + 5k2 = -12k + 12k

Combine like terms: -12k + 12k = 0
-16 + 12k + 5k2 = 0

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

Divide each side by '5'.
-3.2 + 2.4k + k2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 2.4k + 3.2 + k2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 2.4k + k2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 2.4k + k2 = 0 + 3.2
2.4k + k2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
2.4k + k2 = 3.2

The k term is 2.4k.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4k + 1.44 + k2 = 3.2 + 1.44

Reorder the terms:
1.44 + 2.4k + k2 = 3.2 + 1.44

Combine like terms: 3.2 + 1.44 = 4.64
1.44 + 2.4k + k2 = 4.64

Factor a perfect square on the left side:
(k + 1.2)(k + 1.2) = 4.64

Calculate the square root of the right side: 2.154065923

Break this problem into two subproblems by setting 
(k + 1.2) equal to 2.154065923 and -2.154065923.

Subproblem 1

k + 1.2 = 2.154065923 Simplifying k + 1.2 = 2.154065923 Reorder the terms: 1.2 + k = 2.154065923 Solving 1.2 + k = 2.154065923 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + k = 2.154065923 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + k = 2.154065923 + -1.2 k = 2.154065923 + -1.2 Combine like terms: 2.154065923 + -1.2 = 0.954065923 k = 0.954065923 Simplifying k = 0.954065923

Subproblem 2

k + 1.2 = -2.154065923 Simplifying k + 1.2 = -2.154065923 Reorder the terms: 1.2 + k = -2.154065923 Solving 1.2 + k = -2.154065923 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + k = -2.154065923 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + k = -2.154065923 + -1.2 k = -2.154065923 + -1.2 Combine like terms: -2.154065923 + -1.2 = -3.354065923 k = -3.354065923 Simplifying k = -3.354065923

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.954065923, -3.354065923}

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