SOLUTION: Solve. 5(x-2)^2=3 a. 1/5 19/5 b. 10+-square root15over 5 c. 10+-square root3 over 5 d. +- 59 over 25

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve. 5(x-2)^2=3 a. 1/5 19/5 b. 10+-square root15over 5 c. 10+-square root3 over 5 d. +- 59 over 25       Log On


   

Question 102584: Solve. 5(x-2)^2=3
a. 1/5 19/5
b. 10+-square root15over 5
c. 10+-square root3 over 5
d. +- 59 over 25
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%28x-2%29%5E2=3+ Start with the given equation


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


x-2=0%2B-sqrt%283%2F5%29+ Take the square root of both sides


x-2=0%2B-sqrt%283%29%2Fsqrt%285%29 Break up the root


x-2=%28sqrt%283%29%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29+ Multiply the right side by sqrt%285%29%2Fsqrt%285%29

x-2=0%2B-sqrt%2815%29%2F5+ Combine the roots and multiply


x=2%2B-sqrt%2815%29%2F5 Add 2 to both sides



x=%2810%2B-sqrt%2815%29%29%2F5 Combine the two fractions


So our answer is x=%2810%2B-sqrt%2815%29%29%2F5 which means our answer is B

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
The answer is b 10+-square root15over 5
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