8k^2=4k^2+3k+16

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Solution for 8k^2=4k^2+3k+16 equation:


Simplifying
8k2 = 4k2 + 3k + 16

Reorder the terms:
8k2 = 16 + 3k + 4k2

Solving
8k2 = 16 + 3k + 4k2

Solving for variable 'k'.

Reorder the terms:
-16 + -3k + 8k2 + -4k2 = 16 + 3k + 4k2 + -16 + -3k + -4k2

Combine like terms: 8k2 + -4k2 = 4k2
-16 + -3k + 4k2 = 16 + 3k + 4k2 + -16 + -3k + -4k2

Reorder the terms:
-16 + -3k + 4k2 = 16 + -16 + 3k + -3k + 4k2 + -4k2

Combine like terms: 16 + -16 = 0
-16 + -3k + 4k2 = 0 + 3k + -3k + 4k2 + -4k2
-16 + -3k + 4k2 = 3k + -3k + 4k2 + -4k2

Combine like terms: 3k + -3k = 0
-16 + -3k + 4k2 = 0 + 4k2 + -4k2
-16 + -3k + 4k2 = 4k2 + -4k2

Combine like terms: 4k2 + -4k2 = 0
-16 + -3k + 4k2 = 0

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

Divide each side by '4'.
-4 + -0.75k + k2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.75k + 4 + k2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.75k + k2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.75k + k2 = 0 + 4
-0.75k + k2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.75k + k2 = 4

The k term is -0.75k.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75k + 0.140625 + k2 = 4 + 0.140625

Reorder the terms:
0.140625 + -0.75k + k2 = 4 + 0.140625

Combine like terms: 4 + 0.140625 = 4.140625
0.140625 + -0.75k + k2 = 4.140625

Factor a perfect square on the left side:
(k + -0.375)(k + -0.375) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(k + -0.375) equal to 2.034852575 and -2.034852575.

Subproblem 1

k + -0.375 = 2.034852575 Simplifying k + -0.375 = 2.034852575 Reorder the terms: -0.375 + k = 2.034852575 Solving -0.375 + k = 2.034852575 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + k = 2.034852575 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + k = 2.034852575 + 0.375 k = 2.034852575 + 0.375 Combine like terms: 2.034852575 + 0.375 = 2.409852575 k = 2.409852575 Simplifying k = 2.409852575

Subproblem 2

k + -0.375 = -2.034852575 Simplifying k + -0.375 = -2.034852575 Reorder the terms: -0.375 + k = -2.034852575 Solving -0.375 + k = -2.034852575 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + k = -2.034852575 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + k = -2.034852575 + 0.375 k = -2.034852575 + 0.375 Combine like terms: -2.034852575 + 0.375 = -1.659852575 k = -1.659852575 Simplifying k = -1.659852575

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.409852575, -1.659852575}

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