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Answer:
The solution to the quadratic equation:
[tex]x=0,\:x=30[/tex]
Step-by-step explanation:
Given the equation
[tex]6x-0.2x^2=0[/tex]
6x - 0.2x · x = 0
Factor out common term -x
-x (0.2x - 6) = 0
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
[tex]x=0\quad \mathrm{or}\quad \:0.2x-6=0[/tex]
solving
[tex]0.2x-6=0[/tex]
Multiply both sides by 10
[tex]0.2x\cdot \:10-6\cdot \:10=0\cdot \:10[/tex]
Refine
[tex]2x-60=0[/tex]
Add 60 to both sides
[tex]2x-60+60=0+60[/tex]
Simplify
[tex]2x=60[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{60}{2}[/tex]
Simplify
[tex]x=30[/tex]
Thus, the solution to the quadratic equation:
[tex]x=0,\:x=30[/tex]