Question

Resolva a equação literal:

x² - 6ax = 16a²

Answer 1

x²-6ax=16a²
x²-6ax-16a²=0 

a=1
b=-6a
c=-16a2

Δ=b²-4ac
Δ=(-6a)²-4(-16a²)
Δ=36a²+64a²
Δ=100a²
√Δ=√100a²=±10a

$x= \frac{-(-6a)\pm10a}{2} = \frac{6a\pm10a}{2} \\ \\ x'= \frac{6a+10a}{2} = \frac{16a}{2} =8a \\ \\ x"= \frac{6a-10a}{2} =- \frac{4a}{2} =-2a$

Answer 2

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$\sf x^2-6ax=16a^2\\\sf x^2-6ax+\boxed{\sf (3a)^2}=16a^2+\boxed{\sf (3a)^2}\\\sf (x-3a)^2=16a^2+9a^2\\\sf (x-3a)^2=25a^2\\\sf x-3a=\pm\sqrt{25a^2}\\\sf x-3a=\pm5a\\\sf x-3a=5a\\\sf x=5a+3a\\\sf x=8a\\\sf x-3a=-5a\\\sf x=3a-5a\\\sf x=-2a\\\huge\boxed{\boxed{\boxed{\boxed{\sf S=\{-2a,8a\}}}}}$