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

1 Answer
Alan P.
Aug 10, 2015

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)

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