SOLUTION: I have an equation (2x^2)-7=0. The answer I have been given is the square root of 14 over 2. I'm unsure why. Could you walk me through the steps please?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I have an equation (2x^2)-7=0. The answer I have been given is the square root of 14 over 2. I'm unsure why. Could you walk me through the steps please?      Log On


   

Question 221155: I have an equation (2x^2)-7=0. The answer I have been given is the square root of 14 over 2. I'm unsure why. Could you walk me through the steps please?
Found 4 solutions by stanbon, chibisan, rapaljer, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(2x^2)-7=0
-----------------------
Add 7 to both sides to get:
(2x^2) = 7
Divide both sides by 2 to get:
x^2 = 7/2
------
Multiply numerator and denominator of the fraction by 2
to get:
x^2 = 14/4
---
Take the square root of both sides to get:
x = [sqrt(14)]/2
=======================================
Cheers,
Stan H.

Answer by chibisan(131) About Me  (Show Source):
You can put this solution on YOUR website!
(2x^2)-7 = 0
bring -7 to R.H.S
2x^2 = 7
x^2 = 7/2
+x+=+sqrt%287%2F2%29+
(probably the answer you were given is wrong)

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2 -7=0
2x^2 =7
x^2=7/2
x=0%2B-sqrt%287%2F2%29
x=0%2B-sqrt%287%29%2Fsqrt%282%29

The trick now is to rationalize the denominator, by multiplying numerator and denominator by square root of 2:
x=0%2B-sqrt%287%29%2Fsqrt%282%29*%28%28sqrt%282%29%29%2F%28sqrt%282%29%29%29+++
x=0%2B-sqrt%2814%29%2F2

R^2

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
I have an equation (2x^2)-7=0. The answer I have been given is the square root of 14 over 2. I'm unsure why. Could you walk me through the steps please?

2x%5E2+-+7+=+0

2x%5E2+=+7 ------- Adding 7 to both sides of equation

%282x%5E2%29%2F2+=+7%2F2 ------- Dividing both sides of equation by 2

x%5E2+=+7%2F2

sqrt%28x%5E2%29+=+sqrt%287%2F2%29 ----- x%5E2+=+sqrt%287%29%2Fsqrt%282%29
This could be the answer, but since you have a different answer, it's quite obvious that they want you to RATIONALIZE the denominator (not leaving the denominator with a square root value).

So, x%5E2+=+sqrt%287%29%2Fsqrt%282%29

x%5E2+=+%28sqrt%287%29%2Asqrt%282%29%29%2F%28sqrt%282%29%2Asqrt%282%29%29 ------ Rationalizing denominator

Therefore, we get: x%5E2+=+sqrt%287%2A2%29%2F2, or: highlight_green%28sqrt%2814%29%2F2%29