Question 465444
A quadratic equation is one in which the
highest power of {{{x}}} is {{{2}}}.
This will automatically happen when you 
multiply something like {{{ (x + 2)*(x -7) }}}
You get {{{ x^2 - 5x - 14 }}}
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Now suppose you have 2 solutions to a 
quadratic equation, 
(1) {{{ x = 8 }}}
(2) {{{ x = 4/5 }}}
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Subtract {{{8}}} from both sides of (1)
(1) {{{ x - 8 = 0 }}}
Subtract {{{ 4/5}}} from both sides of (2)
(2) {{{ x - 4/5 = 0 }}}
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The key now is that if you multiply (1) and (2),
you will have {{{ 0*0 = 0}}}, so
{{{ (x-8)*(x-4/5) = 0 }}}
Now do the multiplication
{{{ x^2 - 8x - (4/5)*x + 32/5 = 0 }}}
Multiply both sides by {{{5}}}
{{{ 5x^2 - 40x - 4x + 32 = 0 }}}
{{{ 5x^2 - 44x + 32 = 0 }}} answer
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Now you can check the answer
Does {{{ x = 4/5 }}} work?
{{{ 5*(4/5)^2 - 44*(4/5) + 32 = 0 }}}
{{{ 5*(16/25) - 44*(20/25) + 32 = 0 }}}
Multiply both sides by {{{ 25 }}}
{{{ 80 - 880 + 800 = 0 }}}
{{{ 880 - 880 = 0 }}}
{{{ 0 = 0 }}}
OK
You can check the other solution