SOLUTION: -16t^2-12t=2 I know the answer but I need help figuring out how to get to the answer. Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: -16t^2-12t=2 I know the answer but I need help figuring out how to get to the answer. Thank you.      Log On


   

Question 574640: -16t^2-12t=2
I know the answer but I need help figuring out how to get to the answer. Thank you.
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-16t%5E2-12t=2 Start with the given equation.


-16t%5E2-12t-2=0 Get every term to the left side.


Notice that the quadratic -16t%5E2-12t-2 is in the form of At%5E2%2BBt%2BC where A=-16, B=-12, and C=-2


Let's use the quadratic formula to solve for "t":


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


t+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%28-16%29%28-2%29+%29%29%2F%282%28-16%29%29 Plug in A=-16, B=-12, and C=-2


t+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%28-16%29%28-2%29+%29%29%2F%282%28-16%29%29 Negate -12 to get 12.


t+=+%2812+%2B-+sqrt%28+144-4%28-16%29%28-2%29+%29%29%2F%282%28-16%29%29 Square -12 to get 144.


t+=+%2812+%2B-+sqrt%28+144-128+%29%29%2F%282%28-16%29%29 Multiply 4%28-16%29%28-2%29 to get 128


t+=+%2812+%2B-+sqrt%28+16+%29%29%2F%282%28-16%29%29 Subtract 128 from 144 to get 16


t+=+%2812+%2B-+sqrt%28+16+%29%29%2F%28-32%29 Multiply 2 and -16 to get -32.


t+=+%2812+%2B-+4%29%2F%28-32%29 Take the square root of 16 to get 4.


t+=+%2812+%2B+4%29%2F%28-32%29 or t+=+%2812+-+4%29%2F%28-32%29 Break up the expression.


t+=+%2816%29%2F%28-32%29 or t+=++%288%29%2F%28-32%29 Combine like terms.


t+=+-1%2F2 or t+=+-1%2F4 Simplify.


So the solutions are t+=+-1%2F2 or t+=+-1%2F4


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+-16t%5E2+-+12t+=+2+
Divide both sides by 2
+-8t%5E2+-+6t+=+1+
Divide both sides by +-8+
+t%5E2+%2B+%283%2F4%29%2At+=+-%281%2F8%29+
Complete the square
Take +1%2F2+ of the coefficient of x,
square it, and add it to both sides
+t%5E2+%2B+%283%2F4%29%2At+%2B+%283%2F8%29%5E2+=+-%281%2F8%29+%2B+%283%2F8%29%5E2+
+%28+t+%2B+3%2F8+%29%5E2+=+-8%2F64+%2B+9%2F64+
+%28+t+%2B+3%2F8+%29%5E2+=+1%2F64+
take the square root of both sides ( both + and - roots )
+t+%2B+3%2F8+=+1%2F8+
+t+=+-%281%2F4%29+
and
+t+%2B+3%2F8+=+-%281%2F8%29+
+t+=+-%281%2F2%29+
----------------
check the answers:
+-16t%5E2+-+12t+=+2+
+-16%28-1%2F4%29%5E2+-+12%2A%28-1%2F4%29+=+2+
+-1+%2B+3+=+2+
+2+=+2+
and
+-16%2A%28-1%2F2%29%5E2+-+12%2A%28-1%2F2%29+=+2+
+-4+%2B+6+=+2+
+2+=+2+
OK