c^2-100+20c=0

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Solution for c^2-100+20c=0 equation:


Simplifying
c2 + -100 + 20c = 0

Reorder the terms:
-100 + 20c + c2 = 0

Solving
-100 + 20c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 20c + 100 + c2 = 0 + 100

Reorder the terms:
-100 + 100 + 20c + c2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 20c + c2 = 0 + 100
20c + c2 = 0 + 100

Combine like terms: 0 + 100 = 100
20c + c2 = 100

The c term is 20c.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20c + 100 + c2 = 100 + 100

Reorder the terms:
100 + 20c + c2 = 100 + 100

Combine like terms: 100 + 100 = 200
100 + 20c + c2 = 200

Factor a perfect square on the left side:
(c + 10)(c + 10) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(c + 10) equal to 14.142135624 and -14.142135624.

Subproblem 1

c + 10 = 14.142135624 Simplifying c + 10 = 14.142135624 Reorder the terms: 10 + c = 14.142135624 Solving 10 + c = 14.142135624 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + c = 14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + c = 14.142135624 + -10 c = 14.142135624 + -10 Combine like terms: 14.142135624 + -10 = 4.142135624 c = 4.142135624 Simplifying c = 4.142135624

Subproblem 2

c + 10 = -14.142135624 Simplifying c + 10 = -14.142135624 Reorder the terms: 10 + c = -14.142135624 Solving 10 + c = -14.142135624 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + c = -14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + c = -14.142135624 + -10 c = -14.142135624 + -10 Combine like terms: -14.142135624 + -10 = -24.142135624 c = -24.142135624 Simplifying c = -24.142135624

Solution

The solution to the problem is based on the solutions from the subproblems. c = {4.142135624, -24.142135624}

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