Solve {l}{text{Persamaangarissinggungkurva}y=sqrt{2x-1}text{di}}{text{titikberabsis}5text{adalah}ldots}{{llll}{text{A.}x-3y=-14}&{text{D.}3x+y=4}}

$$\left. \begin{array} { l } { \text { Persamaan garis singgung kurva } y = \sqrt { 2 x - 1 } \text { di } } \\ { \text { titik berabsis } 5 \text { adalah } \ldots } \\ { \left. \begin{array} { l l l l } { \text { A. } x - 3 y = - 14 } & { \text { D. } 3 x + y = 4 } \end{array} \right. } \end{array} \right.$$

Solve for x

$$x=\frac{y^{2}+1}{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{2x-1}=y$$

Square both sides of the equation.

$$2x-1=y^{2}$$

Add 1 to both sides of the equation.

$$2x-1-\left(-1\right)=y^{2}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$2x=y^{2}-\left(-1\right)$$

Subtract -1 from y^{2}.

$$2x=y^{2}+1$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y^{2}+1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y^{2}+1}{2}$$

Solve for x (complex solution)

$$x=\frac{y^{2}+1}{2}$$

$$arg(y)<\pi \text{ or }y=0$$