Question 582171
{{{ H = .005s^2 + .007s - .031 }}}
given:
{{{ 200 = .005s^2 + .007s - .031 }}}
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Multiply both sides by {{{ 1000 }}}
{{{ 200000 = 5s^2 + 7s - 31 }}}
{{{ 5s^2 + 7s - 200031 = 0 }}}
{{{ 5s^2 + 7s = 200031 }}}
Divide both sides by {{{5}}}
{{{ s^2 + (7/5)*s = 200031/5 }}}
I'll try completing the square
{{{ s^2 + (7/5)*s + (7/10)^2 = 200031/5 + (7/10)^2 }}}
{{{ s^2 + (7/5)*s + 49/100 = 200031/5 + 49/100 }}}
{{{ s^2 + (7/5)*s + 49/100 = 4000620/100 + 49/100 }}}
{{{ s^2 + (7/5)*s + 49/100 = 4000669/100 }}}
{{{ ( s + .7 )^2 = ( 2000.1672/10 )^2 }}}
Take the square root of both sides
{{{ s + .7 = 200.01672 }}}
{{{ s = 200.01672 - .7 }}}
{{{ s = 199.31672 }}}
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I'll check this
{{{ H = .005*199.32^2 + .007*199.32 - .031 }}}
{{{ H = .005*39728.462 + 1.395 - .031 }}}
{{{ H = 198.642 + 1.395 - .031 }}}
{{{ H = 200.0063 }}}
This seems very close to the right answer.
Are we both making the same mistake?
The other possibility is you copied the 
problem wrong ( or your teacher did ).
Did anyone get the right answer?