document.write( "Question 555668: xsquared+x-6 how do you get the trinomial completely and need this very soon. Thank You \n" ); document.write( "

Algebra.Com's Answer #361893 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you mean \"How do you complete the square?\"
\n" ); document.write( "I do not really know what you meant to ask, but I am going to try to answer, anyway.
\n" ); document.write( " $\"x%5E2%2Bx-6\"$ has 3 terms, so it is a trinomial.
\n" ); document.write( "It's degree is 2, so it can be called a quadratic trinomial, or a quadratic polynomial.
\n" ); document.write( " $\"f%28x%29=x%5E2%2Bx-6\"$ would be called a quadratic function, and
\n" ); document.write( " $\"x%5E2%2Bx-6=0\"$ would be called a quadratic equation.
\n" ); document.write( "The sum of terms $\"x%5E2%2Bx\"$ can be considered to be part of the square
\n" ); document.write( " $\"%28x%2B1%2F2%29%5E2=x%5E2%2Bx%2B1%2F4\"$
\n" ); document.write( "That trick is often called \"completing the square.\"
\n" ); document.write( "That is useful for finding the axis of symmetry and vertex of the curve (called a parabola) described by $\"f%28x%29=x%5E2%2Bx-6\"$ .
\n" ); document.write( "It is also useful for solving quadratic equations.
\n" ); document.write( " $\"f%28x%29=x%5E2%2Bx-6=x%5E2%2Bx%2B1%2F4-1%2F4-6=%28x%2B1%2F2%29%5E2-25%2F4\"$
\n" ); document.write( "That tells you that the function has a minimum (and the parabola has a vertex) at
\n" ); document.write( " $\"x=-1%2F2\"$ with $\"f%28-1%2F2%29=-25%2F4\"$
\n" ); document.write( "Similarly $\"x%5E2%2Bx-6=0\"$ can be written as
\n" ); document.write( " $\"%28x%2B1%2F2%29%5E2-25%2F4=0\"$ or $\"%28x%2B1%2F2%29%5E2=25%2F4\"$ and solved to get
\n" ); document.write( " $\"x=-1%2F2+%2B-+sqrt%2825%2F4%29=-1%2F2+%2B-+5%2F2\"$ , which gives you $\"x=2\"$ and $\"x=-3\"$ as solutions. \n" ); document.write( "

\n" );