document.write( "Question 216874: solve the equation by completing the square: $\"4x%5E2%2B40x%2B280=0\"$ \n" ); document.write( "

Algebra.Com's Answer #163688 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
solve the equation by completing the square: 4x^2 + 40x + 280 = 0
\n" ); document.write( "4x^2 + 40x + ___ = -280
\n" ); document.write( ":
\n" ); document.write( "Divide both sides by 4
\n" ); document.write( "x^2 + 10x + ____ = -70
\n" ); document.write( ":
\n" ); document.write( "Find the value of the 3rd term that completes the square
\n" ); document.write( "using the coefficient of x: (10/2)^2 = 25
\n" ); document.write( "x^2 + 10x + 25 = -70 + 25
\n" ); document.write( ":
\n" ); document.write( "x^2 + 10x + 25 = -45
\n" ); document.write( ":
\n" ); document.write( "Which is:
\n" ); document.write( "(x + 5)^2 = -45
\n" ); document.write( ":
\n" ); document.write( "Find the square root of both sides
\n" ); document.write( "x + 5 = +/- $\"sqrt%28-45%29\"$
\n" ); document.write( ":
\n" ); document.write( "x + 5 = +/- $\"sqrt%289%2A-1%2A5%29\"$
\n" ); document.write( ":
\n" ); document.write( "Extract the square root of -1 and 9
\n" ); document.write( "x + 5 = +/- $\"3i%2Asqrt%285%29\"$
\n" ); document.write( ":
\n" ); document.write( "Two solutions
\n" ); document.write( " $\"x+=+-5+%2B+3i%2Asqrt%285%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=+-5+-+3i%2Asqrt%285%29\"$
\n" ); document.write( " \n" ); document.write( "

\n" );