2c^2-7c=5

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Solution for 2c^2-7c=5 equation:


Simplifying
2c2 + -7c = 5

Reorder the terms:
-7c + 2c2 = 5

Solving
-7c + 2c2 = 5

Solving for variable 'c'.

Reorder the terms:
-5 + -7c + 2c2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -7c + 2c2 = 0

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

Divide each side by '2'.
-2.5 + -3.5c + c2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -3.5c + 2.5 + c2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -3.5c + c2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -3.5c + c2 = 0 + 2.5
-3.5c + c2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-3.5c + c2 = 2.5

The c term is -3.5c.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5c + 3.0625 + c2 = 2.5 + 3.0625

Reorder the terms:
3.0625 + -3.5c + c2 = 2.5 + 3.0625

Combine like terms: 2.5 + 3.0625 = 5.5625
3.0625 + -3.5c + c2 = 5.5625

Factor a perfect square on the left side:
(c + -1.75)(c + -1.75) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(c + -1.75) equal to 2.358495283 and -2.358495283.

Subproblem 1

c + -1.75 = 2.358495283 Simplifying c + -1.75 = 2.358495283 Reorder the terms: -1.75 + c = 2.358495283 Solving -1.75 + c = 2.358495283 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = 2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = 2.358495283 + 1.75 c = 2.358495283 + 1.75 Combine like terms: 2.358495283 + 1.75 = 4.108495283 c = 4.108495283 Simplifying c = 4.108495283

Subproblem 2

c + -1.75 = -2.358495283 Simplifying c + -1.75 = -2.358495283 Reorder the terms: -1.75 + c = -2.358495283 Solving -1.75 + c = -2.358495283 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = -2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = -2.358495283 + 1.75 c = -2.358495283 + 1.75 Combine like terms: -2.358495283 + 1.75 = -0.608495283 c = -0.608495283 Simplifying c = -0.608495283

Solution

The solution to the problem is based on the solutions from the subproblems. c = {4.108495283, -0.608495283}

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