Simplifying
c2 + 3.75c + -1 = 0
Reorder the terms:
-1 + 3.75c + c2 = 0
Solving
-1 + 3.75c + c2 = 0
Solving for variable 'c'.
Begin completing the square.
Move the constant term to the right:
Add '1' to each side of the equation.
-1 + 3.75c + 1 + c2 = 0 + 1
Reorder the terms:
-1 + 1 + 3.75c + c2 = 0 + 1
Combine like terms: -1 + 1 = 0
0 + 3.75c + c2 = 0 + 1
3.75c + c2 = 0 + 1
Combine like terms: 0 + 1 = 1
3.75c + c2 = 1
The c term is 3.75c. Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.
Add '3.515625' to each side of the equation.
3.75c + 3.515625 + c2 = 1 + 3.515625
Reorder the terms:
3.515625 + 3.75c + c2 = 1 + 3.515625
Combine like terms: 1 + 3.515625 = 4.515625
3.515625 + 3.75c + c2 = 4.515625
Factor a perfect square on the left side:
(c + 1.875)(c + 1.875) = 4.515625
Calculate the square root of the right side: 2.125
Break this problem into two subproblems by setting
(c + 1.875) equal to 2.125 and -2.125.
Subproblem 1
c + 1.875 = 2.125
Simplifying
c + 1.875 = 2.125
Reorder the terms:
1.875 + c = 2.125
Solving
1.875 + c = 2.125
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-1.875' to each side of the equation.
1.875 + -1.875 + c = 2.125 + -1.875
Combine like terms: 1.875 + -1.875 = 0.000
0.000 + c = 2.125 + -1.875
c = 2.125 + -1.875
Combine like terms: 2.125 + -1.875 = 0.25
c = 0.25
Simplifying
c = 0.25
Subproblem 2
c + 1.875 = -2.125
Simplifying
c + 1.875 = -2.125
Reorder the terms:
1.875 + c = -2.125
Solving
1.875 + c = -2.125
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-1.875' to each side of the equation.
1.875 + -1.875 + c = -2.125 + -1.875
Combine like terms: 1.875 + -1.875 = 0.000
0.000 + c = -2.125 + -1.875
c = -2.125 + -1.875
Combine like terms: -2.125 + -1.875 = -4
c = -4
Simplifying
c = -4
Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.25, -4}
