4k(k+3)=19

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Solution for 4k(k+3)=19 equation:


Simplifying
4k(k + 3) = 19

Reorder the terms:
4k(3 + k) = 19
(3 * 4k + k * 4k) = 19
(12k + 4k2) = 19

Solving
12k + 4k2 = 19

Solving for variable 'k'.

Reorder the terms:
-19 + 12k + 4k2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + 12k + 4k2 = 0

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

Divide each side by '4'.
-4.75 + 3k + k2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 3k + 4.75 + k2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 3k + k2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 3k + k2 = 0 + 4.75
3k + k2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
3k + k2 = 4.75

The k term is 3k.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3k + 2.25 + k2 = 4.75 + 2.25

Reorder the terms:
2.25 + 3k + k2 = 4.75 + 2.25

Combine like terms: 4.75 + 2.25 = 7
2.25 + 3k + k2 = 7

Factor a perfect square on the left side:
(k + 1.5)(k + 1.5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(k + 1.5) equal to 2.645751311 and -2.645751311.

Subproblem 1

k + 1.5 = 2.645751311 Simplifying k + 1.5 = 2.645751311 Reorder the terms: 1.5 + k = 2.645751311 Solving 1.5 + k = 2.645751311 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + k = 2.645751311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = 2.645751311 + -1.5 k = 2.645751311 + -1.5 Combine like terms: 2.645751311 + -1.5 = 1.145751311 k = 1.145751311 Simplifying k = 1.145751311

Subproblem 2

k + 1.5 = -2.645751311 Simplifying k + 1.5 = -2.645751311 Reorder the terms: 1.5 + k = -2.645751311 Solving 1.5 + k = -2.645751311 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + k = -2.645751311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = -2.645751311 + -1.5 k = -2.645751311 + -1.5 Combine like terms: -2.645751311 + -1.5 = -4.145751311 k = -4.145751311 Simplifying k = -4.145751311

Solution

The solution to the problem is based on the solutions from the subproblems. k = {1.145751311, -4.145751311}

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