Question

solve for x. you may use your calculator or desmos. $sqrt{2x + 5} = x + 1$

Explanation:

Step1: Square both sides to eliminate root

$$(\sqrt{2x+5})^2=(x+1)^2$$
$$2x+5=x^2+2x+1$$

Step2: Rearrange to quadratic form

$$x^2+2x+1-2x-5=0$$
$$x^2-4=0$$

Step3: Factor and solve for x

$$(x-2)(x+2)=0$$
$$x=2 \text{ or } x=-2$$

Step4: Verify solutions in original equation

For $x=2$: $\sqrt{2(2)+5}=\sqrt{9}=3$, $2+1=3$ (valid)
For $x=-2$: $\sqrt{2(-2)+5}=\sqrt{1}=1$, $-2+1=-1$ (invalid, since $1
eq-1$)

Answer:

$x=2$