How do you solve sqrt(3x+10)= 5-2x3x+10=52x?

1 Answer
Apr 11, 2016

x_(1,2)={3/4,5}x1,2={34,5}

Explanation:

sqrt(3x+10)=5-2x3x+10=52x

(sqrt(3x+10))^2=(5-2x)^2(3x+10)2=(52x)2

3x+10=(5-2x)^23x+10=(52x)2

3x+10=25-20x+4x^23x+10=2520x+4x2

4x^2-20x+25-3x-10=04x220x+253x10=0

4x^2-23x+15=04x223x+15=0

ax^2+bx+c=0ax2+bx+c=0

Delta=sqrt(b^2-4*a*c)

Delta=sqrt((-23)^2-4*4*15)
Delta=sqrt(529-240)
Delta=sqrt(289)
Delta=17

x_1=(-b-Delta)/(2*a)

x_1=(23-17)/(2*4)

x_1=6/8" "x_1=3/4

x_2=(-b+Delta)/(2*a)

x_2=(23+17)/(2*4)

x_2=20/8

x_2=5

x_(1,2)={3/4,5}