document.write( "Question 1009738: If I have the quadratic function, f(x)= (x^2)-x-12, and I want to find the x-intercept, I have to set y = 0, and factor like so: 0 = (x-4)(x+3).\r
\n" ); document.write( "\n" ); document.write( "The questions is: why can't I complete the square or factor like so: 0 = x(x-1)-12 (which leads to 0 = (x-1)(x-12))? Doing either of those alternative techniques results in different x-intercepts. \n" ); document.write( "

Algebra.Com's Answer #625189 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
You're not doing the algebra right. Completing
\n" ); document.write( "the square should work, though.
\n" ); document.write( " $\"+x%5E2+-+x+-+12+=+0+\"$
\n" ); document.write( " $\"+x%5E2+-+x+=12+\"$
\n" ); document.write( " $\"+x%5E2+-+x+%2B+%28-1%2F2%29%5E2+=+12+%2B+%28-1%2F2%29%5E2+\"$
\n" ); document.write( " $\"+x%5E2+-+x+%2B+1%2F4+=+12+%2B+1%2F4+\"$
\n" ); document.write( " $\"+x%5E2+-+x+%2B+1%2F4+=+49%2F4+\"$
\n" ); document.write( " $\"+%28+x+-+1%2F2+%29%5E2+=+%287%2F2%29%5E2+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( "(1) $\"+x+-+1%2F2+=+7%2F2+\"$
\n" ); document.write( "and, also:
\n" ); document.write( "(2) $\"+x+-+1%2F2+=+-7%2F2+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "(1) $\"+x+=+8%2F2+\"$
\n" ); document.write( "(1) $\"+x+=+4+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+x+=+-6%2F2+\"$
\n" ); document.write( "(2) $\"+x+=+-3+\"$
\n" ); document.write( "------------------
\n" ); document.write( "So, the factors are:
\n" ); document.write( " $\"+%28+x+-+4+%29%2A%28+x+%2B+3+%29+=+0+\"$
\n" ); document.write( "You could also use the quadratic formula \n" ); document.write( "

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