# Solve for v v^2+(v+7)^2=(v+9)^2

v2+(v+7)2=(v+9)2
Simplify (v+9)2.
Rewrite (v+9)2 as (v+9)(v+9).
v2+(v+7)2=(v+9)(v+9)
Expand (v+9)(v+9) using the FOIL Method.
Apply the distributive property.
v2+(v+7)2=v(v+9)+9(v+9)
Apply the distributive property.
v2+(v+7)2=v⋅v+v⋅9+9(v+9)
Apply the distributive property.
v2+(v+7)2=v⋅v+v⋅9+9v+9⋅9
v2+(v+7)2=v⋅v+v⋅9+9v+9⋅9
Simplify and combine like terms.
Simplify each term.
Multiply v by v.
v2+(v+7)2=v2+v⋅9+9v+9⋅9
Move 9 to the left of v.
v2+(v+7)2=v2+9⋅v+9v+9⋅9
Multiply 9 by 9.
v2+(v+7)2=v2+9v+9v+81
v2+(v+7)2=v2+9v+9v+81
Add 9v and 9v.
v2+(v+7)2=v2+18v+81
v2+(v+7)2=v2+18v+81
v2+(v+7)2=v2+18v+81
Move all terms containing v to the left side of the equation.
Subtract v2 from both sides of the equation.
v2+(v+7)2-v2=18v+81
Subtract 18v from both sides of the equation.
v2+(v+7)2-v2-18v=81
Combine the opposite terms in v2+(v+7)2-v2-18v.
Subtract v2 from v2.
(v+7)2+0-18v=81
Add (v+7)2 and 0.
(v+7)2-18v=81
(v+7)2-18v=81
Simplify each term.
Rewrite (v+7)2 as (v+7)(v+7).
(v+7)(v+7)-18v=81
Expand (v+7)(v+7) using the FOIL Method.
Apply the distributive property.
v(v+7)+7(v+7)-18v=81
Apply the distributive property.
v⋅v+v⋅7+7(v+7)-18v=81
Apply the distributive property.
v⋅v+v⋅7+7v+7⋅7-18v=81
v⋅v+v⋅7+7v+7⋅7-18v=81
Simplify and combine like terms.
Simplify each term.
Multiply v by v.
v2+v⋅7+7v+7⋅7-18v=81
Move 7 to the left of v.
v2+7⋅v+7v+7⋅7-18v=81
Multiply 7 by 7.
v2+7v+7v+49-18v=81
v2+7v+7v+49-18v=81
Add 7v and 7v.
v2+14v+49-18v=81
v2+14v+49-18v=81
v2+14v+49-18v=81
Subtract 18v from 14v.
v2-4v+49=81
v2-4v+49=81
Move 81 to the left side of the equation by subtracting it from both sides.
v2-4v+49-81=0
Subtract 81 from 49.
v2-4v-32=0
Factor v2-4v-32 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 -32 and whose sum is -4.
-8,4
Write the factored form using these integers.
(v-8)(v+4)=0
(v-8)(v+4)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
v-8=0
v+4=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
v-8=0
Add 8 to both sides of the equation.
v=8
v=8
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
v+4=0
Subtract 4 from both sides of the equation.
v=-4
v=-4
The final solution is all the values that make (v-8)(v+4)=0 true.
v=8,-4
Solve for v v^2+(v+7)^2=(v+9)^2

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