# Solve for B 36=1/2*(B(B+1))

36=12⋅(B(B+1))
Rewrite the equation as 12⋅(B(B+1))=36.
12⋅(B(B+1))=36
Multiply both sides of the equation by 2.
2⋅12⋅(B(B+1))=2⋅36
Simplify both sides of the equation.
Simplify 2⋅12⋅(B(B+1)).
Cancel the common factor of 2.
Cancel the common factor.
2⋅12⋅(B(B+1))=2⋅36
Rewrite the expression.
1⋅(B(B+1))=2⋅36
1⋅(B(B+1))=2⋅36
Multiply B(B+1) by 1.
B(B+1)=2⋅36
Apply the distributive property.
B⋅B+B⋅1=2⋅36
Simplify the expression.
Multiply B by B.
B2+B⋅1=2⋅36
Multiply B by 1.
B2+B=2⋅36
B2+B=2⋅36
B2+B=2⋅36
Multiply 2 by 36.
B2+B=72
B2+B=72
Move 72 to the left side of the equation by subtracting it from both sides.
B2+B-72=0
Factor B2+B-72 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -72 and whose sum is 1.
-8,9
Write the factored form using these integers.
(B-8)(B+9)=0
(B-8)(B+9)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
B-8=0
B+9=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
B-8=0
Add 8 to both sides of the equation.
B=8
B=8
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
B+9=0
Subtract 9 from both sides of the equation.
B=-9
B=-9
The final solution is all the values that make (B-8)(B+9)=0 true.
B=8,-9
Solve for B 36=1/2*(B(B+1))

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