SOLUTION: Which of the following are solutions to the equation below? Check all that apply. (5x - 2)2 = 10 A. x = -sqrt 10 + 2 /5 B. x = -sqrt 12/5 C. x = sqrt 10 + 2 /5 D. x = -sq

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Which of the following are solutions to the equation below? Check all that apply. (5x - 2)2 = 10 A. x = -sqrt 10 + 2 /5 B. x = -sqrt 12/5 C. x = sqrt 10 + 2 /5 D. x = -sq      Log On


   

Question 949465: Which of the following are solutions to the equation below? Check all that apply.
(5x - 2)2 = 10
A. x = -sqrt 10 + 2 /5
B. x = -sqrt 12/5
C. x = sqrt 10 + 2 /5
D. x = -sqrt 2 +2
E. x = sqrt 12/5
F. x = sqrt 2 + 2
Found 3 solutions by MathLover1, josgarithmetic, Theo:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%285x+-+2%29%5E2+=+10........take square root of both sides
sqrt%28%285x+-+2%29%5E2+%29=+sqrt%2810%29
%285x+-+2%29=+sqrt%2810%29 or -%285x+-+2%29=+sqrt%2810%29
if 5x+-+2=+sqrt%2810%29, then
5x+=+sqrt%2810%29%2B2
x+=+sqrt%2810%29%2F5%2B2%2F5
if -%285x+-+2%29=+sqrt%2810%29, then
-5x+%2B+2=+sqrt%2810%29
2-sqrt%2810%29=5x or
5x=2-sqrt%2810%29
x=2%2F5-sqrt%2810%29%2F5 or x=-sqrt%2810%29%2F5%2B2%2F5
so, your solutions are:
A. x+=+-sqrt%2810%29+%2B+2%2F5
and
C. x+=+sqrt+%2810%29+%2B+2%2F5


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The 2 looks like a factor and needs to be written (5x - 2)^2 = 10.

Simply reversing everything done to x, and doing so to BOTH sides of the equation, will give solutions for x.

What was done to x?
multiplied by 5;
added negative 2;
squared;
All of that set equal to 10.

What to do to solve?
Undo everything going in reverse of the sequence of steps.

ANSWER: NONE of the choices listed is correct.
You should find the solution is equivalent to 2%2F5%2B-+sqrt%2810%29%2F5.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
selection C looks good.

x = (sqrt(10) + 2) / 5

start with (5x-2)^2 = 10

take the square root of both sides of the equation to get:

5x-2 = plus or minus sqrt(10)

add 2 to both sides to get 5x = 2 plus or minus sqrt(10)

divide both sides by 5 to get x = (2 plus or minus sqrt(10)) / 5

if you break the solution up into it's constituent parts, you get:

x = (-sqrt(10) + 2) / 5
or
x = (sqrt(10) + 2) / 5

that looks like selections A and C except you didn't show the parentheses that belong there because it's the whole thing divided by 5, not just the 2.