(3.2-b)*b=2.56

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Solution for (3.2-b)*b=2.56 equation:

Simplifying
(3.2 + -1b) * b = 2.56
Reorder the terms for easier multiplication:
b(3.2 + -1b) = 2.56
(3.2 * b + -1b * b) = 2.56
(3.2b + -1b2) = 2.56
Solving
3.2b + -1b2 = 2.56
Solving for variable 'b'.
Reorder the terms:
-2.56 + 3.2b + -1b2 = 2.56 + -2.56
Combine like terms: 2.56 + -2.56 = 0.00
-2.56 + 3.2b + -1b2 = 0.00
Begin completing the square. Divide all terms by
-1 the coefficient of the squared term:
Divide each side by '-1'.
2.56 + -3.2b + b2 = 0.00
Move the constant term to the right:
Add '-2.56' to each side of the equation.
2.56 + -3.2b + -2.56 + b2 = 0.00 + -2.56
Reorder the terms:
2.56 + -2.56 + -3.2b + b2 = 0.00 + -2.56
Combine like terms: 2.56 + -2.56 = 0.00
0.00 + -3.2b + b2 = 0.00 + -2.56
-3.2b + b2 = 0.00 + -2.56
Combine like terms: 0.00 + -2.56 = -2.56
-3.2b + b2 = -2.56
The b term is -3.2b. Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.
Add '2.56' to each side of the equation.
-3.2b + 2.56 + b2 = -2.56 + 2.56
Reorder the terms:
2.56 + -3.2b + b2 = -2.56 + 2.56
Combine like terms: -2.56 + 2.56 = 0.00
2.56 + -3.2b + b2 = 0.00
Factor a perfect square on the left side:
(b + -1.6)(b + -1.6) = 0.00
Calculate the square root of the right side: 0.00
Break this problem into two subproblems by setting
(b + -1.6) equal to 0.00 and 0.00.
Subproblem 1b + -1.6 = 0.00
Simplifying
b + -1.6 = 0.00
Reorder the terms:
-1.6 + b = 0.00
Solving
-1.6 + b = 0.00
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '1.6' to each side of the equation.
-1.6 + 1.6 + b = 0.00 + 1.6
Combine like terms: -1.6 + 1.6 = 0.0
0.0 + b = 0.00 + 1.6
b = 0.00 + 1.6
Combine like terms: 0.00 + 1.6 = 1.6
b = 1.6
Simplifying
b = 1.6
Subproblem 2b + -1.6 = 0.00
Simplifying
b + -1.6 = 0.00
Reorder the terms:
-1.6 + b = 0.00
Solving
-1.6 + b = 0.00
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '1.6' to each side of the equation.
-1.6 + 1.6 + b = 0.00 + 1.6
Combine like terms: -1.6 + 1.6 = 0.0
0.0 + b = 0.00 + 1.6
b = 0.00 + 1.6
Combine like terms: 0.00 + 1.6 = 1.6
b = 1.6
Simplifying
b = 1.6
SolutionThe solution to the problem is based on the solutions
from the subproblems.
b = {1.6, 1.6}`