b^2+7b-25=12

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Solution for b^2+7b-25=12 equation:


Simplifying
b2 + 7b + -25 = 12

Reorder the terms:
-25 + 7b + b2 = 12

Solving
-25 + 7b + b2 = 12

Solving for variable 'b'.

Reorder the terms:
-25 + -12 + 7b + b2 = 12 + -12

Combine like terms: -25 + -12 = -37
-37 + 7b + b2 = 12 + -12

Combine like terms: 12 + -12 = 0
-37 + 7b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 7b + 37 + b2 = 0 + 37

Reorder the terms:
-37 + 37 + 7b + b2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 7b + b2 = 0 + 37
7b + b2 = 0 + 37

Combine like terms: 0 + 37 = 37
7b + b2 = 37

The b term is 7b.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7b + 12.25 + b2 = 37 + 12.25

Reorder the terms:
12.25 + 7b + b2 = 37 + 12.25

Combine like terms: 37 + 12.25 = 49.25
12.25 + 7b + b2 = 49.25

Factor a perfect square on the left side:
(b + 3.5)(b + 3.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(b + 3.5) equal to 7.017834424 and -7.017834424.

Subproblem 1

b + 3.5 = 7.017834424 Simplifying b + 3.5 = 7.017834424 Reorder the terms: 3.5 + b = 7.017834424 Solving 3.5 + b = 7.017834424 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = 7.017834424 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = 7.017834424 + -3.5 b = 7.017834424 + -3.5 Combine like terms: 7.017834424 + -3.5 = 3.517834424 b = 3.517834424 Simplifying b = 3.517834424

Subproblem 2

b + 3.5 = -7.017834424 Simplifying b + 3.5 = -7.017834424 Reorder the terms: 3.5 + b = -7.017834424 Solving 3.5 + b = -7.017834424 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = -7.017834424 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = -7.017834424 + -3.5 b = -7.017834424 + -3.5 Combine like terms: -7.017834424 + -3.5 = -10.517834424 b = -10.517834424 Simplifying b = -10.517834424

Solution

The solution to the problem is based on the solutions from the subproblems. b = {3.517834424, -10.517834424}

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