How do you solve sqrt(8x+1)=x+2√8x+1=x+2?
1 Answer
Mar 25, 2018
Explanation:
color(blue)"square both sides"square both sides
(sqrt(8x+1))^2=(x+2)^2(√8x+1)2=(x+2)2
rArr8x+1=x^2+4x+4⇒8x+1=x2+4x+4
"rearrange into "color(blue)"standard form"rearrange into standard form
rArrx^2-4x+3=0⇒x2−4x+3=0
"The factors of + 3 which sum to - 4 are - 1 and - 3"The factors of + 3 which sum to - 4 are - 1 and - 3
rArr(x-1)(x-3)=0⇒(x−1)(x−3)=0
"equate each factor to zero and solve for x"equate each factor to zero and solve for x
x-1=0rArrx=1x−1=0⇒x=1
x-3=0rArrx=3x−3=0⇒x=3
color(blue)"As a check"As a check Substitute these values into the equation and if both sides are equal then they are the solutions.
x=1rArrsqrt9=3" and "1+2=3 color(white)(x)✔︎
x=3rArrsqrt25=5" and "3+2=5color(white)(x)✔︎
rArrx=1" or "x=3" are the solutions"
