document.write( "Question 613669: to solve by completing the square, what value should you add to each side of the equation? x^2+20x=-4 \n" ); document.write( "
Algebra.Com's Answer #386150 by Theo(13342)\"\" \"About 
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x^2+20x=-4
\n" ); document.write( "you take 1/2 the value of the coefficient of the b term and you square it and add it to the other side of the equation.
\n" ); document.write( "you start with x^2 + 20x = -4
\n" ); document.write( "the standard form of a quadratic equation is:
\n" ); document.write( "ax^2 + bx + c = 0
\n" ); document.write( "your equation is:
\n" ); document.write( "x^2 + 20x = -4
\n" ); document.write( "add 4 to both sides to get it into the standard form of:
\n" ); document.write( "x^2 + 20x + 4 = 0
\n" ); document.write( "that makes:
\n" ); document.write( "a = 1
\n" ); document.write( "b = 20
\n" ); document.write( "c = 4
\n" ); document.write( "1/2 of 20 = 10
\n" ); document.write( "your equation is x^2 + 20x = -4
\n" ); document.write( "after taking 1/2 the coefficient of the b term, you will get:
\n" ); document.write( "(x + 10)^2 = -4 + 10^2 which becomes:
\n" ); document.write( "(x + 10)^2 = 96
\n" ); document.write( "you then take the square root of both sides of this equation to get:
\n" ); document.write( "x + 10 = +/- sqrt(96)
\n" ); document.write( "you then subtract 10 from both sides of this equation to get:
\n" ); document.write( "x = -10 +/- sqrt(96)
\n" ); document.write( "if you use the quadratic formula instead, you would wind up with the same answer.
\n" ); document.write( "example:
\n" ); document.write( "standard form of your equation is:
\n" ); document.write( "x^2 + 20x + 4 = 0
\n" ); document.write( "a = 1
\n" ); document.write( "b = 20
\n" ); document.write( "c = 4
\n" ); document.write( "quadratic formula is:
\n" ); document.write( "x = (-b +/- sqrt(b^2-4ac))/2a
\n" ); document.write( "plugging in the values, you get:
\n" ); document.write( "x = (-20 +/- sqrt(400-4*1*4))/2 which becomes:
\n" ); document.write( "x = (-20 +/- sqrt(384))/2 which becomes:
\n" ); document.write( "x = (-20 +/- sqrt(4*96))/2 which becomes:
\n" ); document.write( "x = (-20 +/- 2*sqrt(96))/2 which becomes:
\n" ); document.write( "x = -10 +/- sqrt(96).
\n" ); document.write( "you get the same answer either way as you should.\r
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