7b+0.5b^2=120

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Solution for 7b+0.5b^2=120 equation:


Simplifying
7b + 0.5b2 = 120

Solving
7b + 0.5b2 = 120

Solving for variable 'b'.

Reorder the terms:
-120 + 7b + 0.5b2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 7b + 0.5b2 = 0

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-240 + 14b + b2 = 0

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + 14b + 240 + b2 = 0 + 240

Reorder the terms:
-240 + 240 + 14b + b2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + 14b + b2 = 0 + 240
14b + b2 = 0 + 240

Combine like terms: 0 + 240 = 240
14b + b2 = 240

The b term is 14b.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14b + 49 + b2 = 240 + 49

Reorder the terms:
49 + 14b + b2 = 240 + 49

Combine like terms: 240 + 49 = 289
49 + 14b + b2 = 289

Factor a perfect square on the left side:
(b + 7)(b + 7) = 289

Calculate the square root of the right side: 17

Break this problem into two subproblems by setting 
(b + 7) equal to 17 and -17.

Subproblem 1

b + 7 = 17 Simplifying b + 7 = 17 Reorder the terms: 7 + b = 17 Solving 7 + b = 17 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = 17 + -7 Combine like terms: 7 + -7 = 0 0 + b = 17 + -7 b = 17 + -7 Combine like terms: 17 + -7 = 10 b = 10 Simplifying b = 10

Subproblem 2

b + 7 = -17 Simplifying b + 7 = -17 Reorder the terms: 7 + b = -17 Solving 7 + b = -17 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = -17 + -7 Combine like terms: 7 + -7 = 0 0 + b = -17 + -7 b = -17 + -7 Combine like terms: -17 + -7 = -24 b = -24 Simplifying b = -24

Solution

The solution to the problem is based on the solutions from the subproblems. b = {10, -24}

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