How do you solve 2x + sqrt(x+1) = 8?

1 Answer
Prof_S
Mar 2, 2016

x=3 or x=5.25

Explanation:

Subtract 2x from bopth sides of the equation, yielding sqrt(x+1) = 8 -2x. Square both sides of the equation, yielding x+1=64-32x+4x^2. Subtract x+1 from both sides of the equation, yielding 0=63-33x+4x^2.

Using the quadratic equation, one gets
x = (33 (+/-) sqrt(1089 - 4*4*63))/8 = (33 (+/-) sqrt(81))/8 = (33 (+/-) 9)/8.
So, x = 42/8 or x=24/8.

Related questions
See all questions in Radical Equations
Impact of this question
5480 views around the world
You can reuse this answer
Creative Commons License