Question 1036328
<pre>
{{{3-5x = sqrt(5)}}}
Square both sides
{{{(3-5x)^2 = (sqrt(5))^2}}}
Simplify
{{{(3-5x)(3-5x) = 5}}}
{{{9-15x-15x+25x^2=5}}}
{{{9-30x+25x^2=5}}}
Subtract 5 from both sides to get 0 on the right
{{{4-30x+25x^2=0}}}
Rearrange terms in descending order:
{{{25x^2-30x+4=0}}}
Use the quadratic formula:
 {{{x = (-b +- sqrt(b^2-4ac ))/(2a) }}}
 {{{x = (-(-30) +- sqrt((-30)^2-4(25)(4) ))/(2(25)) }}}
 {{{x = (30 +- sqrt(900-400 ))/50 }}}
 {{{x = (30 +- sqrt(500))/50 }}}
 {{{x = (30 +- sqrt(100*5))/50 }}}
 {{{x = (30 +- 10sqrt(5))/50 }}}
Factor out 10 in the numerator:
 {{{x = (10(3 +- sqrt(5)))/50 }}}
Divide top and bottom by 10
 {{{x = (3 +- sqrt(5))/5 }}}

Using the +:

 {{{x = (3 + sqrt(5))/5 }}}
 {{{x = (3 + 2.236)/5 }}}
 {{{x = (5.236)/5 }}}
 {{{x = 1.0472 }}}

Checking in the original equation:

{{{3-5x = sqrt(5)}}}

{{{3-5(1.0472) = 2.236}}}
{{{3-5.236 = 2.236}}}
{{{-2.236 = 2.236}}}

That doesn't check so we must discard  {{{cross(x = (3 + sqrt(5))/5) }}}

Using the -:

 {{{x = (3 - sqrt(5))/5 }}}
 {{{x = (3 - 2.236)/5 }}}
 {{{x = (.764)/5 }}}
 {{{x = 0.1528 }}}

Checking in the original equation:

{{{3-5x = sqrt(5)}}}

{{{3-5(0.1528) = 2.236}}}
{{{3-0.764 = 2.236}}}
{{{2.236 = 2.236}}}

That checks, so the only solution is  {{{x = (3 - sqrt(5))/5 }}}

Note, you must always check equations with square roots
because oftentimes there are extraneous "answers".

Edwin</pre>