SOLUTION: solve the radical equation and check all proposed solutions sqr symbol over 28x+28 = x+8

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Question 1039928: solve the radical equation and check all proposed solutions
sqr symbol over 28x+28 = x+8

Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve the radical equation and check all proposed solutions
sqrt%2828x%2B28%29+=+x%2B8
Square both sides
28x%2B28+=+%28x%2B8%29%5E2
FOIL (x+8)(x+8)
28x%2B28+=+x%5E2%2B16x%2B64
form a quadratic equation on the right
0 = x^2 + 16x - 28x + 64 - 28
0 = x^2 - 12x + 26
This will not factor, use the quadratic formula: a=1; b=-12; c=26
I got approx solutions
x = 2.83772
x = 9.16228
:
Check both solution in the original equation

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve the radical equation and check all proposed solutions
sqr symbol over 28x+28 = x+8
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

sqrt%2828x%2B28%29 = x%2B8

Square both sides
28x%2B28 = %28x%2B8%29%5E2,

28x%2B28 = x%5E2%2B16x%2B64.

Form a quadratic equation on the right

0 = x^2 + 16x - 28x + 64 - 28,

0 = x^2 - 12x + 36,

%28x-6%29%5E2 = 0.

The solution is x = 6 of multiplicity 2.




Figure. Plots y = sqrt%2828x%2B28%29, y = x + 8.