Question

Which quadratic equation is equivalent to (x - 4)2 – ( - 4) - 6 = 0?

Answer 1

Answer:

$u^2-u-6=0$

where

$u=(x-4)$

Step-by-step explanation:

we have

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

Let

$u=(x-4)$

substitute in the expression above

$(u)^2-(u)-6=0$

Solve for u

Complete the square

$(u^2-u+0.25)=6+0.25$

$(u^2-u+0.25)=6.25$

Rewrite as perfect squares

$(u-0.5)^2=6.25$

square root booth sides

$u-0.5=\pm2.5$

$u=0.5\pm2.5$

$u_1=0.5+2.5=3$

$u_2=0.5-2.5=-2$

Solve for x

Remember that

$u=(x-4)$

For u=3

$3=(x-4)$ ----> $x=7$

For u=-2

$-2=(x-4)$ ----> $x=2$