k+4(k+4)=3k(k)

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


Simplifying
k + 4(k + 4) = 3k(k)

Reorder the terms:
k + 4(4 + k) = 3k(k)
k + (4 * 4 + k * 4) = 3k(k)
k + (16 + 4k) = 3k(k)

Reorder the terms:
16 + k + 4k = 3k(k)

Combine like terms: k + 4k = 5k
16 + 5k = 3k(k)

Multiply k * k
16 + 5k = 3k2

Solving
16 + 5k = 3k2

Solving for variable 'k'.

Combine like terms: 3k2 + -3k2 = 0
16 + 5k + -3k2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-5.333333333 + -1.666666667k + k2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -1.666666667k + 5.333333333 + k2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -1.666666667k + k2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -1.666666667k + k2 = 0 + 5.333333333
-1.666666667k + k2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-1.666666667k + k2 = 5.333333333

The k term is -1.666666667k.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667k + 0.6944444447 + k2 = 5.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667k + k2 = 5.333333333 + 0.6944444447

Combine like terms: 5.333333333 + 0.6944444447 = 6.0277777777
0.6944444447 + -1.666666667k + k2 = 6.0277777777

Factor a perfect square on the left side:
(k + -0.8333333335)(k + -0.8333333335) = 6.0277777777

Calculate the square root of the right side: 2.45515331

Break this problem into two subproblems by setting 
(k + -0.8333333335) equal to 2.45515331 and -2.45515331.

Subproblem 1

k + -0.8333333335 = 2.45515331 Simplifying k + -0.8333333335 = 2.45515331 Reorder the terms: -0.8333333335 + k = 2.45515331 Solving -0.8333333335 + k = 2.45515331 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + k = 2.45515331 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + k = 2.45515331 + 0.8333333335 k = 2.45515331 + 0.8333333335 Combine like terms: 2.45515331 + 0.8333333335 = 3.2884866435 k = 3.2884866435 Simplifying k = 3.2884866435

Subproblem 2

k + -0.8333333335 = -2.45515331 Simplifying k + -0.8333333335 = -2.45515331 Reorder the terms: -0.8333333335 + k = -2.45515331 Solving -0.8333333335 + k = -2.45515331 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + k = -2.45515331 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + k = -2.45515331 + 0.8333333335 k = -2.45515331 + 0.8333333335 Combine like terms: -2.45515331 + 0.8333333335 = -1.6218199765 k = -1.6218199765 Simplifying k = -1.6218199765

Solution

The solution to the problem is based on the solutions from the subproblems. k = {3.2884866435, -1.6218199765}

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