document.write( "Question 30991: will you please solve this equation? xSquared-7x+5=0(Completing a square) \n" ); document.write( "
Algebra.Com's Answer #17708 by Fermat(136)\"\" \"About 
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Your eqn is
\n" ); document.write( "x² - 7x + 5 = 0
\n" ); document.write( "When you square a term like (x+a) you get,
\n" ); document.write( "(x+a)² = x² + 2ax + a²
\n" ); document.write( "Look at the coefficient of the x-term. It is 2a. Compare that with the coefficient of the x-term in your own eqn. You have: -7.
\n" ); document.write( "So equate the coefficient values.
\n" ); document.write( "2a = -7
\n" ); document.write( "a = -7/2
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\n" ); document.write( "(x+a)² = (x-7/2)² = x² -7x + 7²/2² = x² -7x + 49/4
\n" ); document.write( "You've got an extra constant term, 49/4, so add and subtract this to keep your original eqn unaltered.
\n" ); document.write( "x² - 7x + 5 = 0 becomes,
\n" ); document.write( "x² -7x + 49/4 - 49/4 + 5 = 0
\n" ); document.write( "(x-7/2)² -49/4 + 20/4 = 0
\n" ); document.write( "(x-7/2)² = 49/4 - 20/4 = 29/4
\n" ); document.write( "(x-7/2)² = 29/4
\n" ); document.write( "Take the square root of both sides,
\n" ); document.write( "(x-7/2) = √29/2
\n" ); document.write( "x = 7/2 +/- √29/2
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\n" ); document.write( "In decimals, that becomes
\n" ); document.write( "x = 3.5 +/- 2.6926
\n" ); document.write( "x = 6.1926, x = 0.8074
\n" ); document.write( "====================== \n" ); document.write( "
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