Question

Which Quadratic equation is equivalent to (x-4)^2-(x-4)-6=0

Answer 1

For this case, we must find the quadratic equation equivalent to:

`(x-4) ^ 2- (x-4) -6 = 0`

By definition we have to:

`(a-b) ^ 2 = a^2-2ab + b ^ 2`

So:

`(x-4) ^ 2 = x ^ 2-2 (x) (4) + 4 ^ 2 = x ^ 2-8x + 16`

So, we have:

`- * + = +\\- * - = +`

`x ^ 2-8x + 16-x + 4-6 = 0`

Equal signs add up and the same sign is placed.

Different signs are subtracted and the sign of the major is placed.

`x ^ 2-9x + 14 = 0`

Answer:

`x ^ 2-9x + 14 = 0`

Answer 2

x²-9x+14 is the quadratic equation.

Explanation:

We have given the equation:

(x-4)²-(x-4)-6=0

We have to find the quadratic equation equivalent to the given equation.So,

(x-4)²-(x-4)-6=0

As we know that, (a-b)²=a²+b²-2ab then we get,

x²+16-8x-x+4-6=0

x²-9x+14=0

x²-9x+14 is the quadratic equation equivalent to (x-4)²-(x-4)-6=0