2c^2-16c=5

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Solution for 2c^2-16c=5 equation:


Simplifying
2c2 + -16c = 5

Reorder the terms:
-16c + 2c2 = 5

Solving
-16c + 2c2 = 5

Solving for variable 'c'.

Reorder the terms:
-5 + -16c + 2c2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -16c + 2c2 = 0

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

Divide each side by '2'.
-2.5 + -8c + c2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -8c + 2.5 + c2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -8c + c2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -8c + c2 = 0 + 2.5
-8c + c2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-8c + c2 = 2.5

The c term is -8c.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8c + 16 + c2 = 2.5 + 16

Reorder the terms:
16 + -8c + c2 = 2.5 + 16

Combine like terms: 2.5 + 16 = 18.5
16 + -8c + c2 = 18.5

Factor a perfect square on the left side:
(c + -4)(c + -4) = 18.5

Calculate the square root of the right side: 4.301162634

Break this problem into two subproblems by setting 
(c + -4) equal to 4.301162634 and -4.301162634.

Subproblem 1

c + -4 = 4.301162634 Simplifying c + -4 = 4.301162634 Reorder the terms: -4 + c = 4.301162634 Solving -4 + c = 4.301162634 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = 4.301162634 + 4 Combine like terms: -4 + 4 = 0 0 + c = 4.301162634 + 4 c = 4.301162634 + 4 Combine like terms: 4.301162634 + 4 = 8.301162634 c = 8.301162634 Simplifying c = 8.301162634

Subproblem 2

c + -4 = -4.301162634 Simplifying c + -4 = -4.301162634 Reorder the terms: -4 + c = -4.301162634 Solving -4 + c = -4.301162634 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = -4.301162634 + 4 Combine like terms: -4 + 4 = 0 0 + c = -4.301162634 + 4 c = -4.301162634 + 4 Combine like terms: -4.301162634 + 4 = -0.301162634 c = -0.301162634 Simplifying c = -0.301162634

Solution

The solution to the problem is based on the solutions from the subproblems. c = {8.301162634, -0.301162634}

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