## Intermediate Algebra for College Students (7th Edition)

$x=3$ or $x=0$
Square both sides of the equation to obtain: $5x+1=(x+1)^2$ Use the rule $(a+b)^2 = a62 + 2ab+b^2$ where $a=x$ and $b=1$ to obtain: $\\5x+1=x^2+2x+1$ Move all terms to the right side of the equation. Note that when a term is moved to the other side of the equation, its sign changes to its opposite. $0=x^2+2x+1-5x-1 \\0=x^2-3x$ Factor the binomial to obtain: $0=x(x-3)$ Equate each factor to zero then solve each equation to obtain: $x = 0 \text{ or } x -3 = 0 \\x = 0 \text{ or } x = 3$