Question

# Solve the equation (\sqrt{x^{2}-3x})=2x-6, inequality, or system of equations.

Equations
Solve the equation $$(\sqrt{x^{2}-3x})=2x-6$$, inequality, or system of equations.

2021-06-11

Step 1
To solve the equation: $$(\sqrt{x^{2}-3x})=2x-6$$
Solution:
$$(\sqrt{x^{2}-3x})=2x-6$$
on squaring both sides we get:
$$\Rightarrow (\sqrt{x^{2}-3x})^{2}=(2x-6)^{2}$$
$$\Rightarrow x^{2}-3x=(2x)^{2}-2(2x)(6)+6^{2}$$
$$\Rightarrow x^{2}-3x=4x^{2}-24x+36$$
$$\Rightarrow x^{2}-4x^{2}-3x+24x-36=0$$
$$\Rightarrow -3x^{2}+21x-36=0$$
$$\Rightarrow -3x^{2}+12x+9x-36=0$$
$$\Rightarrow -3x(x-4)+9(x-4)=0$$
$$\Rightarrow (x-4)(-3x+9)=0$$
$$\Rightarrow (x-4)=0, or (-3x+9)=0$$
$$\Rightarrow x=4, or 3x=9. \Rightarrow x=3$$
Step 2
Result:
Required solutions are, $$x=\{3,4\}$$