Question 1079735
Did I understand this right?
The square of a positive number is increased
by 3 times that number, and the result is 54
OK?
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Let the unknown positive number  = {{{ x }}}
given:
{{{ x^2 + 3x = 54 }}}
Subtract {{{ 54 }}} from both sides
{{{ x^2 + 3x - 54 = 0 }}}
This is a quadratic equation, and it has to
be factored. Then you will have 2 solutions
for {{{x}}}
The form ofthe solution will look like this:
{{{ ( x + j )*( x - k ) = 0 }}} 
where {{{j}}} and {{{k}}} are unkown for the moment
Notice that {{{ 54 = 6*9 }}}. 
{{{6}}} and {{{ 9 }}} will be my {{{j}}} and {{{k}}}
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{{{ ( x + 9 )*( x - 6 ) = 0 }}}
Now expand the left side
{{{ x^2 + 9x - 6x - 54 = 0 }}}
{{{ x^2 + 3x - 54 = 0 }}}
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In order for the left side to be true, either
{{{ x = 6 }}} or
{{{ x = -9 }}}
You are looking for a positive number, so the
answer is {{{ x = 6 }}}
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check answer:
Square the number:
{{{ x^2 = 6^2 }}}
{{{ x^2 = 36 }}}
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Now add 3 times that number
{{{ 36 + 3*6 = 36 + 18 }}}
{{{ 36 + 18 = 54 }}}
which is correct
Hope this helps