document.write( "Question 558089: how do you solve 3=2x^2=5x \n" ); document.write( "

Algebra.Com's Answer #362912 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3=2x%5E2=5x\"$ is two equations, and there is no solution that will work for both.
\n" ); document.write( "You probably meant $\"3=2x%5E2-5x\"$
\n" ); document.write( "From $\"3=2x%5E2-5x\"$
\n" ); document.write( "subtracting 3 from both sides, we get
\n" ); document.write( " $\"0=2x%5E2-5x-3\"$ or $\"2x%5E2-5x-3=0\"$
\n" ); document.write( "That is a quadratic equation.
\n" ); document.write( "ONE WAY TO SOLVE IT
\n" ); document.write( "One of the ways to solve this particular quadratic equation is by factoring. If you are skilled at factoring polynomials, you could figure out that
\n" ); document.write( " $\"2x%5E2-5x-3=%282x%2B1%29%28x-3%29\"$ and can write the equation as
\n" ); document.write( " $\"%282x%2B1%29%28x-3%29=0\"$
\n" ); document.write( "The solutions are values of $\"x\"$ that make one of those factors zero.
\n" ); document.write( "From $\"2x%2B1=0\"$ we get $\"x=-1%2F2\"$
\n" ); document.write( "and from $\"x-3=0\"$ we get $\"x=3\"$
\n" ); document.write( "ANOTHER WAY
\n" ); document.write( "A way that works for all quadratic equations is using the quadratic formula
\n" ); document.write( "For any equation of the form $\"ax%5E2%2Bbx%2Bc=0\"$ the solutions are given by
\n" ); document.write( " $\"x\"$ = $\"%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "For $\"2x%5E2-5x-3=0\"$ , $\"a=2\"$ , $\"b=-5\"$ and $\"c=-3\"$
\n" ); document.write( "The quadratic formula gives you
\n" ); document.write( " $\"x\"$ = $\"%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A%28-3%29+%29%29%2F%282%2A2%29+\"$ = $\"%285+%2B-+sqrt%28+25%2B24+%29%29%2F4+\"$ = $\"%285+%2B-+sqrt%2849%29%29%2F4+\"$ = $\"%285+%2B-+7%29%2F4+\"$
\n" ); document.write( "That gives you $\"x\"$ = $\"%285%2B7%29%2F4\"$ = $\"12%2F4\"$ = $\"3%29%29%29+and%0D%0A%7B%7B%7Bx\"$ = $\"%285-7%29%2F4\"$ = $\"-2%2F4\"$ = $\"-1%2F2\"$
\n" ); document.write( "AND YET ANOTHER WAY
\n" ); document.write( "If you do not like using the quadratic formula, you can \"complete the square.\" The idea behind the \"complete the square\" trick is changing your equation so that you have the square of a binomial on one side of the equal sign and a number on the other side.
\n" ); document.write( "From $\"2x%5E2-5x=3\"$ , you look at $\"2x%5E2-5x\"$
\n" ); document.write( "and figure out what to add to it to make the square of a binomial appear there.
\n" ); document.write( "It could go like this
\n" ); document.write( " $\"2x%5E2-5x=3\"$ --> $\"x%5E2-%285%2F2%29x=3%2F2\"$ (dividing both sides by 2)
\n" ); document.write( " $\"x%5E2-%285%2F2%29x%2B25%2F16=3%2F2%2B25%2F16\"$ adding 25/16 to both sides,
\n" ); document.write( "to make $\"%28x-5%2F4%29%5E2\"$ = $\"x%5E2-2%285%2F4%29x%2B25%2F16\"$ = $\"x%5E2-%285%2F2%29x%2B25%2F16\"$ appear on the left side of the equal sign.
\n" ); document.write( "Then, replacing $\"%28x-5%2F4%29%5E2\"$ for the equivalent expression $\"x%5E2-%285%2F2%29x%2B25%2F16\"$ , the equation transforms into
\n" ); document.write( " $\"%28x-5%2F4%29%5E2\"$ = $\"3%2F2%2B25%2F16\"$ --> $\"%28x-5%2F4%29%5E2\"$ = $\"49%2F16\"$ --> $\"%28x-5%2F4%29%5E2\"$ = $\"%287%2F4%29%5E2\"$
\n" ); document.write( "The solutions would be
\n" ); document.write( " $\"x-5%2F4=7%2F4\"$ --> $\"x=5%2F4%2B7%2F4\"$ --> $\"x=12%2F4\"$ --> $\"x=3\"$ and
\n" ); document.write( " $\"x-5%2F4=-7%2F4\"$ --> $\"x=5%2F4-7%2F4\"$ --> $\"x=-2%2F4\"$ --> $\"x=-1%2F2\"$ \n" ); document.write( "

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