SOLUTION: Give exact and approximate solutions to three decimal places. y^2-4y+4=9 Thank you!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Give exact and approximate solutions to three decimal places. y^2-4y+4=9 Thank you!      Log On


   

Question 221482: Give exact and approximate solutions to three decimal places.
y^2-4y+4=9
Thank you!
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y%5E2-4y%2B4=9 Start with the given equation.


y%5E2-4y%2B4-9=0 Subtract 9 from both sides.


y%5E2-4y-5=0 Combine like terms.


Notice that the quadratic y%5E2-4y-5 is in the form of Ay%5E2%2BBy%2BC where A=1, B=-4, and C=-5


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


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


y+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-4, and C=-5


y+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


y+=+%284+%2B-+sqrt%28+16-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


y+=+%284+%2B-+sqrt%28+16--20+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-5%29 to get -20


y+=+%284+%2B-+sqrt%28+16%2B20+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--20%29 as sqrt%2816%2B20%29


y+=+%284+%2B-+sqrt%28+36+%29%29%2F%282%281%29%29 Add 16 to 20 to get 36


y+=+%284+%2B-+sqrt%28+36+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%284+%2B-+6%29%2F%282%29 Take the square root of 36 to get 6.


y+=+%284+%2B+6%29%2F%282%29 or y+=+%284+-+6%29%2F%282%29 Break up the expression.


y+=+%2810%29%2F%282%29 or y+=++%28-2%29%2F%282%29 Combine like terms.


y+=+5 or y+=+-1 Simplify.


So the solutions are y+=+5 or y+=+-1

If you need more help with this subject, check out this solver.

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
y^2 -4y +4 = 9
.
y^2 -4y -5 =0,,,,,,,,,,factor
.
(y-5)(y+1) =0
.
y= 5,,,-1
.
.
check,,,,(5),,,5^2 -4*5 +4 = 9,,,,,25-20 +4 =9,,,,ok
.
(-1),,,,(-1)^2 -4(-1) +4 = 1+4+4 =9,,,,,,ok
.
.
If we use thew quadratic formula
.
a= 1,,,,b=-4,,,,c=-5
.
x=[ -(-4) +/- sqrt{ (-4)^2 -4(1)(-5)}] / 2(1)
.
x=[4 +/- sqrt{ 16+20}]/2
.
x=[ 4+/- sqrt36] /2
.
x= [4 +/- 6] /2
.
x= 10/2=5,,,,,,-2/2=-1
.