Answer:
x = 0 or -1.5
Step-by-step explanation:
You want to know the values of x that make the equation true:
0.1x = 0.2x(x +2)
It is often convenient to eliminate fractions from an equation you want to solve. Here, you can do that by multiplying by 10.
x = 2x(x +2)
Subtracting x and simplifying the equation gives you the standard-form quadratic ...
2x² +4x -x = 0 . . . . . eliminate parentheses and subtract x
2x² +3x = 0 . . . . . . simplify
This is solved nicely by factoring.
x(2x +3) = 0
Solutions will make the factors zero:
x = 0 . . . . makes the first factor zero
2x +3 = 0 ⇒ x = -3/2 . . . . makes the second factor zero
The values of x that make the equation true are 0 and -1.5.
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Additional comment
The "zero product rule" tells you a product is only zero if it has a factor that is zero.
An equation is formed of two equal expressions. The value of x that satisfies the given equation is -4.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation 0.1x=0.2x(x+2) can be solved for x as shown below.
0.1x = 0.2x ( x + 2 )
Divide both sides of the equation by 0.2x,
0.1x/0.2x = [0.2x(x+2)] / 0.2x
0.5x = x + 2
Bring like terms on the same side of the equation,
0.5x - x = 2
-0.5x = 2
Divide both sides of the equation by (-0.5x),
-0.5x /(-0.5) = 2/(-0.5)
x = -4
Hence, the value of x that satisfies the given equation is -4.
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