How do you solve sqrt(2x+8) = x?
2 Answers
x=4
Explanation:
to get rid of the square root on the right you square both sides so
Then bring
now you can do the quadratic formula to find the zeroes
Explanation:
color(blue)"square both sides"
"note that "sqrtaxxsqrta=(sqrta)^2=a
rArr2x+8=x^2
"rearrange into "color(blue)"standard form ";ax^2+bx+c=0
"subtract "2x+8" from both sides"
0=x^2-2x-8
"the factors of - 8 which sum to - 2 are - 4 and + 2"
rArr0=(x-4)(x+2)
"equate each factor to zero and solve for x"
x+2=0rArrx=-2
x-4=0rArrx=4
color(blue)"As a check" Substitute these values into the left side of the equation and if equal to the right side then they are the solution.
x=-2tosqrt(-4+8)=sqrt4=2!=-2
rArrx=-2" is an extraneous solution"
x=4tosqrt(8+8)=sqrt16=4=" right side"
rArrx=4" is the solution"
If you plot it as