document.write( "Question 151721: What is the actual quadratic formula, and how would you actually get the quation itself? All formulas have a reason to how it was made. Such as, a stated theorem.\r
\n" ); document.write( "\n" ); document.write( "This is an any book question. \n" ); document.write( "
Algebra.Com's Answer #111534 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
What is the actual quadratic formula, and how would you actually get the equation itself? All formulas have a reason to how it was made. Such as, a stated theorem.
\n" ); document.write( ":
\n" ); document.write( "consider ax^2 = bx + c = 0
\n" ); document.write( ":
\n" ); document.write( "solve this by completing the square of the left side, we have:
\n" ); document.write( "\"x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29\" = 0
\n" ); document.write( ";
\n" ); document.write( "adding \"-c%2Fa\" to both sides and completing the square on the left side:
\n" ); document.write( " \"x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%5E2%2F%284a%5E2%29%29\" = \"%28b%5E2%2F%284a%5E2%29%29+-+%28c%2Fa%29\"
\n" ); document.write( ":
\n" ); document.write( "Now if we factor the left side, using the square root property
\n" ); document.write( "\"%28x+%2B%28b%2F%282a%29%29%29%5E2\" = \"%28b%5E2-4ac%29%2F%284a%5E2%29\"
\n" ); document.write( "Finding the square root of both sides
\n" ); document.write( "\"x+%2B%28b%2F%282a%29%29\" = +/-\"sqrt%28%28b%5E2-4ac%29%2F%284a%5E2%29%29\"
\n" ); document.write( ":
\n" ); document.write( "x = \"%28-b%2F%282a%29%29\" +/- \"sqrt%28b%5E2-4ac%29%2F%282a%29\"
\n" ); document.write( "We end up with the famous quadratic formula, that we all love so well!
\n" ); document.write( "x = \"%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" \n" ); document.write( "
\n" );