document.write( "Question 1013184: Hi, can you help me figure out this equation: Find the zeros of ax^2+bx=y-c by completing the square. \n" ); document.write( "

Algebra.Com's Answer #629399 by fractalier(6550) $\"\"$ $\"About$

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\n" ); document.write( "This is the original equation. ax^2 + bx + c = 0\r
\n" ); document.write( "\n" ); document.write( "Move the loose number to the other side. ax^2 + bx = –c\r
\n" ); document.write( "\n" ); document.write( "Divide through by whatever is multiplied on the squared term.
\n" ); document.write( "Take half of the x-term, and square it. Add the squared term to both sides.\r
\n" ); document.write( "\n" ); document.write( "x^2 + (b/a)x + (b^2/4a^2) = –(c/a) + (b^2/4a^2)\r
\n" ); document.write( "\n" ); document.write( "Simplify on the right-hand side; in this case, simplify by converting to a common denominator. \r
\n" ); document.write( "\n" ); document.write( "x^2 + (b/a)x + (b^2/4a^2) = –(4ac/4a^2) + (b^2/4a^2)\r
\n" ); document.write( "\n" ); document.write( "Convert the left-hand side to square form (and do a bit more simplifying on the right). \r
\n" ); document.write( "\n" ); document.write( "(x + b/2a)^2 = (b^2 – 4ac)/4a^2\r
\n" ); document.write( "\n" ); document.write( "Square-root both sides, remembering to put the \"±\" on the right. \r
\n" ); document.write( "\n" ); document.write( "x + b/2a = ± sqrt(b^2 – 4ac)/2a\r
\n" ); document.write( "\n" ); document.write( "Solve for \"x =\", and simplify as necessary. \r
\n" ); document.write( "\n" ); document.write( "x = [ –b ± sqrt(b^2 – 4ac) ] / 2a \n" ); document.write( "

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