How do you solve the equation and identify any extraneous solutions for $x=sqrt(-7x+8)$ ?

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How do you solve the equation and identify any extraneous solutions for $x=sqrt(-7x+8)$ ?

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Answer 1 · 2015-06-05T19:46:31

I would square both sides and get:
$x^2=-7x+8$
$x^2+7x-8=0$
Solving using the Quadratic Formula you get:
$x_(1,2)=(-7+-sqrt(49+32))/2=(-7+-sqrt(81))/2$
$x_1=(-7-9)/2=-8$
$x_2=(-7+9)/2=1$

substituting back into our original expression we see that only $x_2=1$ can be used.

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How do you solve the equation and identify any extraneous solutions for $x=sqrt(-7x+8)$ ?

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How do you solve the equation and identify any extraneous solutions for $x=sqrt(-7x+8)$ ?