Simplifying
2b2 + -7b + -3 = 0
Reorder the terms:
-3 + -7b + 2b2 = 0
Solving
-3 + -7b + 2b2 = 0
Solving for variable 'b'.
Begin completing the square. Divide all terms by
2 the coefficient of the squared term:
Divide each side by '2'.
-1.5 + -3.5b + b2 = 0
Move the constant term to the right:
Add '1.5' to each side of the equation.
-1.5 + -3.5b + 1.5 + b2 = 0 + 1.5
Reorder the terms:
-1.5 + 1.5 + -3.5b + b2 = 0 + 1.5
Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -3.5b + b2 = 0 + 1.5
-3.5b + b2 = 0 + 1.5
Combine like terms: 0 + 1.5 = 1.5
-3.5b + b2 = 1.5
The b term is -3.5b. 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.
-3.5b + 3.0625 + b2 = 1.5 + 3.0625
Reorder the terms:
3.0625 + -3.5b + b2 = 1.5 + 3.0625
Combine like terms: 1.5 + 3.0625 = 4.5625
3.0625 + -3.5b + b2 = 4.5625
Factor a perfect square on the left side:
(b + -1.75)(b + -1.75) = 4.5625
Calculate the square root of the right side: 2.136000936
Break this problem into two subproblems by setting
(b + -1.75) equal to 2.136000936 and -2.136000936.
Subproblem 1
b + -1.75 = 2.136000936
Simplifying
b + -1.75 = 2.136000936
Reorder the terms:
-1.75 + b = 2.136000936
Solving
-1.75 + b = 2.136000936
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '1.75' to each side of the equation.
-1.75 + 1.75 + b = 2.136000936 + 1.75
Combine like terms: -1.75 + 1.75 = 0.00
0.00 + b = 2.136000936 + 1.75
b = 2.136000936 + 1.75
Combine like terms: 2.136000936 + 1.75 = 3.886000936
b = 3.886000936
Simplifying
b = 3.886000936
Subproblem 2
b + -1.75 = -2.136000936
Simplifying
b + -1.75 = -2.136000936
Reorder the terms:
-1.75 + b = -2.136000936
Solving
-1.75 + b = -2.136000936
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '1.75' to each side of the equation.
-1.75 + 1.75 + b = -2.136000936 + 1.75
Combine like terms: -1.75 + 1.75 = 0.00
0.00 + b = -2.136000936 + 1.75
b = -2.136000936 + 1.75
Combine like terms: -2.136000936 + 1.75 = -0.386000936
b = -0.386000936
Simplifying
b = -0.386000936
Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.886000936, -0.386000936}