2c^2+3=2c+6

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Solution for 2c^2+3=2c+6 equation:


Simplifying
2c2 + 3 = 2c + 6

Reorder the terms:
3 + 2c2 = 2c + 6

Reorder the terms:
3 + 2c2 = 6 + 2c

Solving
3 + 2c2 = 6 + 2c

Solving for variable 'c'.

Reorder the terms:
3 + -6 + -2c + 2c2 = 6 + 2c + -6 + -2c

Combine like terms: 3 + -6 = -3
-3 + -2c + 2c2 = 6 + 2c + -6 + -2c

Reorder the terms:
-3 + -2c + 2c2 = 6 + -6 + 2c + -2c

Combine like terms: 6 + -6 = 0
-3 + -2c + 2c2 = 0 + 2c + -2c
-3 + -2c + 2c2 = 2c + -2c

Combine like terms: 2c + -2c = 0
-3 + -2c + 2c2 = 0

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

Divide each side by '2'.
-1.5 + -1c + c2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1c + 1.5 + c2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1c + c2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1c + c2 = 0 + 1.5
-1c + c2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1c + c2 = 1.5

The c term is -1c.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1c + 0.25 + c2 = 1.5 + 0.25

Reorder the terms:
0.25 + -1c + c2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
0.25 + -1c + c2 = 1.75

Factor a perfect square on the left side:
(c + -0.5)(c + -0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(c + -0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

c + -0.5 = 1.322875656 Simplifying c + -0.5 = 1.322875656 Reorder the terms: -0.5 + c = 1.322875656 Solving -0.5 + c = 1.322875656 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 1.322875656 + 0.5 c = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 c = 1.822875656 Simplifying c = 1.822875656

Subproblem 2

c + -0.5 = -1.322875656 Simplifying c + -0.5 = -1.322875656 Reorder the terms: -0.5 + c = -1.322875656 Solving -0.5 + c = -1.322875656 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -1.322875656 + 0.5 c = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 c = -0.822875656 Simplifying c = -0.822875656

Solution

The solution to the problem is based on the solutions from the subproblems. c = {1.822875656, -0.822875656}

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