B^2+4B-40=0

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Solution for B^2+4B-40=0 equation:


Simplifying
B2 + 4B + -40 = 0

Reorder the terms:
-40 + 4B + B2 = 0

Solving
-40 + 4B + B2 = 0

Solving for variable 'B'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 4B + 40 + B2 = 0 + 40

Reorder the terms:
-40 + 40 + 4B + B2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 4B + B2 = 0 + 40
4B + B2 = 0 + 40

Combine like terms: 0 + 40 = 40
4B + B2 = 40

The B term is 4B.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4B + 4 + B2 = 40 + 4

Reorder the terms:
4 + 4B + B2 = 40 + 4

Combine like terms: 40 + 4 = 44
4 + 4B + B2 = 44

Factor a perfect square on the left side:
(B + 2)(B + 2) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(B + 2) equal to 6.633249581 and -6.633249581.

Subproblem 1

B + 2 = 6.633249581 Simplifying B + 2 = 6.633249581 Reorder the terms: 2 + B = 6.633249581 Solving 2 + B = 6.633249581 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + B = 6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + B = 6.633249581 + -2 B = 6.633249581 + -2 Combine like terms: 6.633249581 + -2 = 4.633249581 B = 4.633249581 Simplifying B = 4.633249581

Subproblem 2

B + 2 = -6.633249581 Simplifying B + 2 = -6.633249581 Reorder the terms: 2 + B = -6.633249581 Solving 2 + B = -6.633249581 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + B = -6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + B = -6.633249581 + -2 B = -6.633249581 + -2 Combine like terms: -6.633249581 + -2 = -8.633249581 B = -8.633249581 Simplifying B = -8.633249581

Solution

The solution to the problem is based on the solutions from the subproblems. B = {4.633249581, -8.633249581}

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