## Intermediate Algebra (6th Edition)

$x=3$
Using the properties of equality, the given equation, $2x+\sqrt{x+1}=8 ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{x+1}=-2x+8 .\end{array} Squaring both sides of the equation above, then the solution/s is/are \begin{array}{l}\require{cancel} x+1=(-2x)^2+2(-2x)(8)+(8)^2 \\\\ x+1=4x^2-32x+64 \\\\ -4x^2+(x+32x)+(1-64)=0 \\\\ -4x^2+33x-63=0 \\\\ 4x^2-33x+63=0 \\\\ (4x-21)(x-3)=0 \\\\ x=\left\{ \dfrac{21}{4},3 \right\} .\end{array} Upon checking, only $x=3$ satisfies the original equation.