(2k+4)(2k+9)=3k(3k)+11k

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Solution for (2k+4)(2k+9)=3k(3k)+11k equation:


Simplifying
(2k + 4)(2k + 9) = 3k(3k) + 11k

Reorder the terms:
(4 + 2k)(2k + 9) = 3k(3k) + 11k

Reorder the terms:
(4 + 2k)(9 + 2k) = 3k(3k) + 11k

Multiply (4 + 2k) * (9 + 2k)
(4(9 + 2k) + 2k * (9 + 2k)) = 3k(3k) + 11k
((9 * 4 + 2k * 4) + 2k * (9 + 2k)) = 3k(3k) + 11k
((36 + 8k) + 2k * (9 + 2k)) = 3k(3k) + 11k
(36 + 8k + (9 * 2k + 2k * 2k)) = 3k(3k) + 11k
(36 + 8k + (18k + 4k2)) = 3k(3k) + 11k

Combine like terms: 8k + 18k = 26k
(36 + 26k + 4k2) = 3k(3k) + 11k

Remove parenthesis around (3k)
36 + 26k + 4k2 = 3k * 3k + 11k

Reorder the terms for easier multiplication:
36 + 26k + 4k2 = 3 * 3k * k + 11k

Multiply 3 * 3
36 + 26k + 4k2 = 9k * k + 11k

Multiply k * k
36 + 26k + 4k2 = 9k2 + 11k

Reorder the terms:
36 + 26k + 4k2 = 11k + 9k2

Solving
36 + 26k + 4k2 = 11k + 9k2

Solving for variable 'k'.

Reorder the terms:
36 + 26k + -11k + 4k2 + -9k2 = 11k + 9k2 + -11k + -9k2

Combine like terms: 26k + -11k = 15k
36 + 15k + 4k2 + -9k2 = 11k + 9k2 + -11k + -9k2

Combine like terms: 4k2 + -9k2 = -5k2
36 + 15k + -5k2 = 11k + 9k2 + -11k + -9k2

Reorder the terms:
36 + 15k + -5k2 = 11k + -11k + 9k2 + -9k2

Combine like terms: 11k + -11k = 0
36 + 15k + -5k2 = 0 + 9k2 + -9k2
36 + 15k + -5k2 = 9k2 + -9k2

Combine like terms: 9k2 + -9k2 = 0
36 + 15k + -5k2 = 0

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

Divide each side by '-5'.
-7.2 + -3k + k2 = 0

Move the constant term to the right:

Add '7.2' to each side of the equation.
-7.2 + -3k + 7.2 + k2 = 0 + 7.2

Reorder the terms:
-7.2 + 7.2 + -3k + k2 = 0 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + -3k + k2 = 0 + 7.2
-3k + k2 = 0 + 7.2

Combine like terms: 0 + 7.2 = 7.2
-3k + k2 = 7.2

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 = 7.2 + 2.25

Reorder the terms:
2.25 + -3k + k2 = 7.2 + 2.25

Combine like terms: 7.2 + 2.25 = 9.45
2.25 + -3k + k2 = 9.45

Factor a perfect square on the left side:
(k + -1.5)(k + -1.5) = 9.45

Calculate the square root of the right side: 3.07408523

Break this problem into two subproblems by setting 
(k + -1.5) equal to 3.07408523 and -3.07408523.

Subproblem 1

k + -1.5 = 3.07408523 Simplifying k + -1.5 = 3.07408523 Reorder the terms: -1.5 + k = 3.07408523 Solving -1.5 + k = 3.07408523 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 = 3.07408523 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = 3.07408523 + 1.5 k = 3.07408523 + 1.5 Combine like terms: 3.07408523 + 1.5 = 4.57408523 k = 4.57408523 Simplifying k = 4.57408523

Subproblem 2

k + -1.5 = -3.07408523 Simplifying k + -1.5 = -3.07408523 Reorder the terms: -1.5 + k = -3.07408523 Solving -1.5 + k = -3.07408523 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 = -3.07408523 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = -3.07408523 + 1.5 k = -3.07408523 + 1.5 Combine like terms: -3.07408523 + 1.5 = -1.57408523 k = -1.57408523 Simplifying k = -1.57408523

Solution

The solution to the problem is based on the solutions from the subproblems. k = {4.57408523, -1.57408523}

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