+0  
 
0
155
1
avatar

3+(x+4)^(1/2)=x

Guest Mar 1, 2017
Sort: 

1+0 Answers

 #1
avatar
0

Solve for x:
3 + sqrt(x + 4) = x

Subtract 3 from both sides:
sqrt(x + 4) = x - 3

Raise both sides to the power of two:
x + 4 = (x - 3)^2

Expand out terms of the right hand side:
x + 4 = x^2 - 6 x + 9

Subtract x^2 - 6 x + 9 from both sides:
-x^2 + 7 x - 5 = 0

Multiply both sides by -1:
x^2 - 7 x + 5 = 0

Subtract 5 from both sides:
x^2 - 7 x = -5

Add 49/4 to both sides:
x^2 - 7 x + 49/4 = 29/4

Write the left hand side as a square:
(x - 7/2)^2 = 29/4

Take the square root of both sides:
x - 7/2 = sqrt(29)/2 or x - 7/2 = -sqrt(29)/2

Add 7/2 to both sides:
x = 7/2 + sqrt(29)/2 or x - 7/2 = -sqrt(29)/2

Add 7/2 to both sides:
x = 7/2 + sqrt(29)/2 or x = 7/2 - sqrt(29)/2

3 + sqrt(x + 4) ⇒ 3 + sqrt(4 + (7/2 - sqrt(29)/2)) = 3 + sqrt(15/2 - sqrt(29)/2) ≈ 5.19258
x ⇒ 7/2 - sqrt(29)/2 = 1/2 (7 - sqrt(29)) ≈ 0.807418:
So this solution is incorrect

3 + sqrt(x + 4) ⇒ 3 + sqrt(4 + (7/2 + sqrt(29)/2)) = 3 + sqrt(1/2 (15 + sqrt(29))) ≈ 6.19258
x ⇒ 7/2 + sqrt(29)/2 = 1/2 (7 + sqrt(29)) ≈ 6.19258:
So this solution is correct

The solution is:
Answer: |x = 7/2 + sqrt(29)/2

Guest Mar 1, 2017

17 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details