# Determine the value(s) of x such that [[x,2,1]][[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]] = 0

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`[[x,2,1]][[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]] = 0`
Multiplying the first two matrices, we have:
`[[-2x,-x+7,2x+5]] [[x],[-1],[2]]=0`
Multiplying these matrices, we have:
`[-2x^2 + x - 7 + 4x + 10] =0`
Or:
`-2x^2 + 5x + 3 = 0`
You can solve this by factoring, or using the quadratic formula:
`(-2x-1)(x-3)=0`
Thus, `x=-1/2` or `x=3`

`[[x,2,1]][[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]]=0`

We need to solve the above equation.

Let's first multiply `[[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]]`.

`[[x,2,1]][[-2x+5],[-x+4],[2x-5]]=0`

Now we have scalar product of two vectors.

`-2x^2+5x-2x+8+2x-5=0`

`-2x^2+5x+3=0`

When we solve this quadratic equation we get

`x_1=1/2` and `x_2=-3`.

**Solutions to** **the equation are** `x_1=1/2` **and** `x_2=-3.`