SOLUTION: I am having a hard time on this multiple choice problem can someone please help me? Solve. 5(x – 2)^2 = 3 a +-59/25 b 1/5,19/5 c 10+-square root 15 over 5 d 10+- squar

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am having a hard time on this multiple choice problem can someone please help me? Solve. 5(x – 2)^2 = 3 a +-59/25 b 1/5,19/5 c 10+-square root 15 over 5 d 10+- squar      Log On


   

Question 103650: I am having a hard time on this multiple choice problem can someone please help me?
Solve. 5(x – 2)^2 = 3
a +-59/25
b 1/5,19/5
c 10+-square root 15 over 5
d 10+- square root 3 over 5
Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
5(x – 2)^2 = 3
5(x^2-4x+4)=3
5x^2-20x+20=3
5x^2-20x+17=0
x=(10+-sqrt(15))/5 (see below)
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-20x%2B17+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-20%29%5E2-4%2A5%2A17=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+60+%29%29%2F2%5C5+=+2.77459666924148
x%5B2%5D+=+%28-%28-20%29-sqrt%28+60+%29%29%2F2%5C5+=+1.22540333075852

Quadratic expression 5x%5E2%2B-20x%2B17 can be factored:
5x%5E2%2B-20x%2B17+=+%28x-2.77459666924148%29%2A%28x-1.22540333075852%29
Again, the answer is: 2.77459666924148, 1.22540333075852. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-20%2Ax%2B17+%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given equation




%28x-2%29%5E2=3%2F5 Divide both sides by 5


Take the square root of both sides



Add 2 to both sides to isolate x.




Break up the root


Multiply by sqrt%285%29%2Fsqrt%285%29 to rationalize the denominator


Multiply



Simplify


Rewrite 2 as 10%2F5


Combine the fractions

-----------------------------------
Answer:

So our solution is:




So the answer is C