Question 1042927
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What value of x will satisfy this equation {{{sqrt(2x)+4=x}}}
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<U>Answer</U>. x = 8.


<U>Solution</U>


<pre>
{{{sqrt(2x)+4}}} = {{{x}}}  --->  {{{sqrt(2x)}}} = {{{x-4}}}  --->  square both sides --->

2x = {{{(x-4)^2}}}  --->  2x = {{{x^2 - 8x + 16}}}  --->  {{{x^2 - 10x + 16}}} = {{{0}}}  --->  factor left side --->

(x-2)*(x-8) = 0.

The roots are x = 2 and x = 8.

The root x = 8 satisfies the original equation.

The root x = 2 does not satisfy the original equation. It is an extraneous solution.
</pre>