4c^2+c=30

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Solution for 4c^2+c=30 equation:


Simplifying
4c2 + c = 30

Reorder the terms:
c + 4c2 = 30

Solving
c + 4c2 = 30

Solving for variable 'c'.

Reorder the terms:
-30 + c + 4c2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + c + 4c2 = 0

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

Divide each side by '4'.
-7.5 + 0.25c + c2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 0.25c + 7.5 + c2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 0.25c + c2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 0.25c + c2 = 0 + 7.5
0.25c + c2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
0.25c + c2 = 7.5

The c term is c.  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.
0.25c + 0.25 + c2 = 7.5 + 0.25

Reorder the terms:
0.25 + 0.25c + c2 = 7.5 + 0.25

Combine like terms: 7.5 + 0.25 = 7.75
0.25 + 0.25c + c2 = 7.75

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(c + 0.5) equal to 2.783882181 and -2.783882181.

Subproblem 1

c + 0.5 = 2.783882181 Simplifying c + 0.5 = 2.783882181 Reorder the terms: 0.5 + c = 2.783882181 Solving 0.5 + c = 2.783882181 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 = 2.783882181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 2.783882181 + -0.5 c = 2.783882181 + -0.5 Combine like terms: 2.783882181 + -0.5 = 2.283882181 c = 2.283882181 Simplifying c = 2.283882181

Subproblem 2

c + 0.5 = -2.783882181 Simplifying c + 0.5 = -2.783882181 Reorder the terms: 0.5 + c = -2.783882181 Solving 0.5 + c = -2.783882181 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 = -2.783882181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -2.783882181 + -0.5 c = -2.783882181 + -0.5 Combine like terms: -2.783882181 + -0.5 = -3.283882181 c = -3.283882181 Simplifying c = -3.283882181

Solution

The solution to the problem is based on the solutions from the subproblems. c = {2.283882181, -3.283882181}

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