Question

How do you solve `sqrt(x + 3) = 2x + 1`?

Answer 1

`x= (-3+-sqrt(41))/8`

Explanation:

Given `sqrt(x+3) = 2x+1`

Square both sides:
`color(white)("XXXX")` `x+3 = 4x^2+4x+1`

Subtract `(x+3)` from both sides (and reverse sides)
`color(white)("XXXX")` `4x^2+3x-2=0`

Using the quadratic formula (see below)
`color(white)("XXXX")` `x= (-3+-sqrt(41))/8`

Quadratic formula:
`color(white)("XXXX")`for any quadratic in the general form:
`color(white)("XXXX")` `color(white)("XXXX")` `ax^2+bx+c=0`
`color(white)("XXXX")`the solutions are given by the formula:
`color(white)("XXXX")` `color(white)("XXXX")` `x = (-b+-sqrt(b^2-4ac))/(2a)`