Square root of 7x + 8 = x
2006-12-10 07:09:12 · 3 answers · asked by crazylifer 3 in Science & Mathematics ➔ Mathematics
sqrt(7x+8) = x
Your first step is to square both sides, effectively removing the square root symbol.
7x + 8 = x^2
Now, move everything over to the left hand side
-x^2 + 7x + 8 = 0
and multiply everything by -1, changing the signs of everything
x^2 - 7x - 8 = 0
Now, we factor as normal
(x - 8) (x + 1) = 0
Solving this gives us x = 8 and x = -1 as solutions.
BUT WAIT! We can't assume both of these solutions will work, so we have to plug this back into the original equation. Square roots do funny things which is why it is ABSOLUTELY NECESSARY to check your answer.
Test x = 8:
sqrt( 7(8) + 8) = 8?
sqrt(56 + 8) = 8?
sqrt(64) = 8? YES!!
Therefore, we keep x = 8 as a value.
Test x = -1
sqrt (7(-1) + 8) = -1?
sqrt (-7 + 8) = -1?
sqrt (1) = -1?
1 = -1? NO!!!
Therefore, we discard x = -1.
Therefore, our only solution is x = 8.
2006-12-10 07:14:21 · answer #1 · answered by Puggy 7 · 0⤊ 0⤋
Square both sides and you get x^2 - 7x - 8=0, then use the quadratic equation to find the solutions: 8, -1.
2006-12-10 15:13:45 · answer #2 · answered by Jordan H 2 · 0⤊ 2⤋
sqr of 7x+8=x,
so you must do
7x+8=x^2
x^2-7x-8=0
(x-8)(x+1)=0
x=8, or 1
2006-12-10 15:14:36 · answer #3 · answered by abcd 2 · 0⤊ 4⤋