30c+c^2=262

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Solution for 30c+c^2=262 equation:


Simplifying
30c + c2 = 262

Solving
30c + c2 = 262

Solving for variable 'c'.

Reorder the terms:
-262 + 30c + c2 = 262 + -262

Combine like terms: 262 + -262 = 0
-262 + 30c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '262' to each side of the equation.
-262 + 30c + 262 + c2 = 0 + 262

Reorder the terms:
-262 + 262 + 30c + c2 = 0 + 262

Combine like terms: -262 + 262 = 0
0 + 30c + c2 = 0 + 262
30c + c2 = 0 + 262

Combine like terms: 0 + 262 = 262
30c + c2 = 262

The c term is 30c.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30c + 225 + c2 = 262 + 225

Reorder the terms:
225 + 30c + c2 = 262 + 225

Combine like terms: 262 + 225 = 487
225 + 30c + c2 = 487

Factor a perfect square on the left side:
(c + 15)(c + 15) = 487

Calculate the square root of the right side: 22.068076491

Break this problem into two subproblems by setting 
(c + 15) equal to 22.068076491 and -22.068076491.

Subproblem 1

c + 15 = 22.068076491 Simplifying c + 15 = 22.068076491 Reorder the terms: 15 + c = 22.068076491 Solving 15 + c = 22.068076491 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + c = 22.068076491 + -15 Combine like terms: 15 + -15 = 0 0 + c = 22.068076491 + -15 c = 22.068076491 + -15 Combine like terms: 22.068076491 + -15 = 7.068076491 c = 7.068076491 Simplifying c = 7.068076491

Subproblem 2

c + 15 = -22.068076491 Simplifying c + 15 = -22.068076491 Reorder the terms: 15 + c = -22.068076491 Solving 15 + c = -22.068076491 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + c = -22.068076491 + -15 Combine like terms: 15 + -15 = 0 0 + c = -22.068076491 + -15 c = -22.068076491 + -15 Combine like terms: -22.068076491 + -15 = -37.068076491 c = -37.068076491 Simplifying c = -37.068076491

Solution

The solution to the problem is based on the solutions from the subproblems. c = {7.068076491, -37.068076491}

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