Question

(2x-3)²=25

SOLUÇÃO DA EQUAÇÃO!

Answer 1

(2x-3)²=25
(2x-3)*(2x-3)=25
4x²-6x-6x+9=25
4x²-12x+9-25=0
4x²-12x-16=0

usando Bhaskara:
a=4,b=-12,c=-16

∆=b²-4ac
∆=(-12)²-4*4*(-16)
∆=144+256
∆=400

x=(-b±√∆)/2a
x=(-(-12)±√400)/2*4
x=(12±20)/8

x'=(12+20)/8
x'=32/8
x'=4

x"=(12-20)/8
x"=-8/8
x"=-1

Answer 2

$(2x-3)\²=25 \\ \\ 2x-3=\± \sqrt{25} \\ \\ 2x'-3= \sqrt{25} \\ \\ 2x'-3=5 \\ \\ 2x'=5+3 \\ \\ 2x'=8 \\ \\ x'= \frac{8}{2} \\ \\ \boxed{x'=4}$


$2x''-3=- \sqrt{25} \\ \\ 2x''-3=-5 \\ \\ 2x''=-5+3 \\ \\ 2x''=-2 \\ \\ x''= \frac{-2}{2} \\ \\ \boxed{x''=-1}$


S={[-1,4}]