What is the value of x in: $(20-2x)(20-2x)x = 576$
What are the step to find the value of x in this equation?$$(20-2x)(20-2x)x = 576$$
I am doing Shaum's pre-calculus and there is this a word problem at the end of the chapter. There is 3 side of a box and the volume, and you have to find the value of x. I tried putting all the terms on one side and do a synthetic division to find x but it didn't work. What is the correct way to solve this problem?
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$\begingroup$Note that the equation can be factorized as
$$(20-2x)(20-2x)x -576$$$$= 4(x^3-20x^2+100x -144)$$$$= 4(x^3-20x^2+64x + 36x -144)$$$$= 4[x(x-16)(x-4)+36(x -4)]$$$$= 4(x-4)(x^2-16x+36)=0$$
which yields the solutions $x=4, \>8\pm 2\sqrt7$.
$\endgroup$ 1 $\begingroup$Notice that $(20-2x)^2 x=24^2$
Since the LHS is equal to a square, it has to be a square itself, which means x could be a square because the product of 2 squares is a square.
i.e. $m^2 *n$ is a square if n is a square.
Trying out a few values of x will fetch the answer,
$x=2^2=4$
and then do the long division to get the other two roots.
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