SOLUTION: solve the equation: (w+2)^2=2w^2+10w+13 for w if there is more than one solution, seperate them with commas

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve the equation: (w+2)^2=2w^2+10w+13 for w if there is more than one solution, seperate them with commas       Log On


   

Question 506871: solve the equation: (w+2)^2=2w^2+10w+13 for w
if there is more than one solution, seperate them with commas
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28w%2B2%29%5E2=2w%5E2%2B10w%2B13

w%5E2%2B4w%2B4=2w%5E2%2B10w%2B13


w%5E2%2B4w%2B4-2w%5E2-10w-13=0 Get every term to the left side.


-w%5E2-6w-9=0 Combine like terms.


Notice that the quadratic -w%5E2-6w-9 is in the form of Aw%5E2%2BBw%2BC where A=-1, B=-6, and C=-9


Let's use the quadratic formula to solve for "w":


w+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


w+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%28-1%29%28-9%29+%29%29%2F%282%28-1%29%29 Plug in A=-1, B=-6, and C=-9


w+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%28-1%29%28-9%29+%29%29%2F%282%28-1%29%29 Negate -6 to get 6.


w+=+%286+%2B-+sqrt%28+36-4%28-1%29%28-9%29+%29%29%2F%282%28-1%29%29 Square -6 to get 36.


w+=+%286+%2B-+sqrt%28+36-36+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-9%29 to get 36


w+=+%286+%2B-+sqrt%28+0+%29%29%2F%282%28-1%29%29 Subtract 36 from 36 to get 0


w+=+%286+%2B-+sqrt%28+0+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


w+=+%286+%2B-+0%29%2F%28-2%29 Take the square root of 0 to get 0.


w+=+%286+%2B+0%29%2F%28-2%29 or w+=+%286+-+0%29%2F%28-2%29 Break up the expression.


w+=+%286%29%2F%28-2%29 or w+=++%286%29%2F%28-2%29 Combine like terms.


w+=+-3 or w+=+-3 Simplify.


So the only solution is w+=+-3