Question

the equation 3x^2-6x=8 is rewritten in a form of 3(x-p)^2+q=0.

Answer 1

Answer:

$3(x - 1)^2 - 11= 0$

Step-by-step explanation:

Given

$3x^2 - 6x = 8$

Required

Rewrite in form of $3(x - p)^2 + q = 0$

$3x^2 - 6x = 8$

Subtract 8 from both sides

$3x^2 - 6x - 8 = 8 - 8$

$3x^2 - 6x - 8 = 0$

Express -8 as 3 - 11;

So, we have:

$3x^2 - 6x + 3 - 11= 0$

Expand $3x^2 - 6x + 3$

$3(x^2 - 2x + 1) - 11= 0$

Factorize the expression in the bracket;

$3(x^2 - x -x + 1) - 11= 0$

$3(x(x - 1) -1(x - 1)) - 11= 0$

$3((x - 1)^2) - 11= 0$

$3(x - 1)^2 - 11= 0$

By comparison: $3(x - p)^2 + q = 0$

$p= 1$

$q = -11$