Respuesta :
You can divide the whole expression by -3:
[tex]-3x^2+24x=27 \iff x^2-8x = -9[/tex]
Recalling that
[tex](x-a)^2=x^2-2ax+a^2[/tex]
Let's compare the middle term:
[tex]-8x = -2ax \iff a=4[/tex]
So, we want to complete
[tex](x-4)^2 = x^2-8x+16[/tex]
Which differs from [tex]x^2-8x[/tex] by 16. So, if we add 16 to both sides, we have
[tex]x^2-8x=-9 \iff x^2-8x+16=7 \iff (x-4)^2=7[/tex]
Answer:
(x - 4)^2 = 7.
Step-by-step explanation:
-3x^2 + 24x = 27
-3(x^2 - 8x) = 27 Divide through by -3:
(x^2 - 8x) = -9 Divide the -8 by 2. Now (x - 4)^2 = x^2 - 8x + 16 so:
(x - 4)^2 - 16 = -9
(x - 4)^2 = 16 - 9
(x - 4)^2 = 7.
