How do you solve $x-1= sqrt( 6x+10)$ ?

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Answer 1 · 2016-11-07T14:05:24

$x = 9$ .

$(x - 1)^2 = (sqrt(6x + 10))^2$

$x^2 - 2x + 1 = 6x + 10$

$x^2 - 8x - 9 = 0$

$(x - 9)(x + 1) = 0$

$x = 9 and x =-1$

However, since extraneous solutions are a distinct possibility, let's check our solution inside the initial equation.

$9 - 1 =^? sqrt(6 xx 9 + 10)$

$8 = 8" "color(green)(√)$

AND

$-1 - 1=^? sqrt(6 xx -1 + 10)$

$-2 != 2" "color(red)(xx)$

Hence, the only true solution is $x = 9$ .

Hopefully this helps!

How do you solve x-1= sqrt( 6x+10)x-1= sqrt( 6x+10)?