document.write( "Question 685998: Solve for x by completing the square
\n" ); document.write( "2x^2+20=4x \n" ); document.write( "

Algebra.Com's Answer #424678 by funmath(2933) $\"\"$ $\"About$

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Solve for x by completing the square
\n" ); document.write( " $\"2x%5E2%2B20=4x\"$
\n" ); document.write( "First get the x's together and the constant on the other side.
\n" ); document.write( " $\"2x%5E2-4x=-20\"$
\n" ); document.write( "Then divide the whole equation by any coefficient in front of the x^2...in this case, 2.
\n" ); document.write( " $\"2x%5E2%2F2-4x%2F2=-20%2F2\"$
\n" ); document.write( " $\"x%5E2-2x=-10\"$
\n" ); document.write( "At this point, if we call the coefficient of x, b....then we would add (b/2)^2 to both sides.
\n" ); document.write( " $\"%28b%2F2%29%5E2=%28-2%2F2%29%5E2\"$ -> $\"%28-1%29%5E2=1\"$
\n" ); document.write( " $\"x%5E2-2x%2B1=-10%2B1\"$
\n" ); document.write( "Factor the left and simplify the right. Perfect squares always factor to be the sqrt or the front and back with the sign that is in front of the x term between them...like this.
\n" ); document.write( " $\"%28x-1%29%5E2=-9\"$
\n" ); document.write( "Take the square root of both sides...don't forget it is always + or -.
\n" ); document.write( " $\"sqrt%28%28x-1%29%5E2%29\"$ =+ or - $\"sqrt%28-9%29\"$
\n" ); document.write( "If you are only allowed to use \"real\" solutions...you are done...there is no \"real\" solution. However, if you are using imaginary or complex numbers...keep going as follows:
\n" ); document.write( "x-1= + or -3i
\n" ); document.write( "x=1 + or -3i
\n" ); document.write( "This is two answers:
\n" ); document.write( " $\"highlight%28x=1-3i%29\"$ or $\"highlight%28x=1%2B3i%29\"$
\n" ); document.write( "Happy Calculating!!!! \n" ); document.write( "

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