How do you solve sqrt(8x+1)=x+2?
1 Answer
Mar 25, 2018
Explanation:
color(blue)"square both sides"
(sqrt(8x+1))^2=(x+2)^2
rArr8x+1=x^2+4x+4
"rearrange into "color(blue)"standard form"
rArrx^2-4x+3=0
"The factors of + 3 which sum to - 4 are - 1 and - 3"
rArr(x-1)(x-3)=0
"equate each factor to zero and solve for x"
x-1=0rArrx=1
x-3=0rArrx=3
color(blue)"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"
