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
