Question

[2.06] Solve the equation 2 over 5 (x − 4) = 2x for x.

−8

negative 1 over 2

1

−1

Answer 1

\[\frac{ 2 }{ 5(x-4) }=2x\]
As you can see, we have a proportion, so, let's first do distributive on that denominator.
\[\frac{ 2 }{ 5x-20 }=2x\]
So, let's pass the whole (5x-20) multiplying to the other side:
\[2=2x(5x-20)\]
with that done, let's apply distributive there:
\[2=10x ^{2}-40x\]
Let's pass that 2 as a negative so we can have everything equal to zero:
\[10x ^{2}-40x-2=0\]
Let's apply the general formula for this situation:
\[x=\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\]
Where:
a=10
b=-40
c=-2
It should look like this:
\[x=\frac{ -(-40)\pm \sqrt{(-40)^{2}-4(10)(-2)} }{ 2(10) }\]
Think you can take over from here? :)

Answer 2

5x^2-20x-1=0
x^2-4x-1/5=0
make it square
x^2-4x+4-4-1/5=0
(x-2)^2-21/5=0
(x-2)^2=21/5
x-2=+-(sqrt(21/5))
x1=sqrt(21/5)
x2=-sqrt(21/5)