document.write( "Question 181102: Can you show me step by step how to complete the square?\r
\n" ); document.write( "\n" ); document.write( "1.) 3t^2 + 24t-13
\n" ); document.write( "2.) 4s^2+s+2
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Algebra.Com's Answer #135777 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
complete the square?
\n" ); document.write( "1.) 3t^2 + 24t-13
\n" ); document.write( "The coefficient of t^2 has to be 1, divide each term by 3, results:
\n" ); document.write( "t^2 + 8t - $\"13%2F3\"$ = 0
\n" ); document.write( ":
\n" ); document.write( "t^2 + 8t + ___ = $\"13%2F3\"$
\n" ); document.write( "Find the term that will complete the square; square half of the coefficient of t
\n" ); document.write( ".5*8=4; 4^2=16; add to both sides
\n" ); document.write( "t^2 + 8t + 16 = $\"13%2F3\"$ + 16
\n" ); document.write( ":
\n" ); document.write( "t^2 + 8t + 9 = $\"13%2F3\"$ + $\"48%2F3\"$ ; change 16 to thirds
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\n" ); document.write( "(t + 4)^2 = $\"61%2F3\"$
\n" ); document.write( "Find the square root of both sides:
\n" ); document.write( "t + 4 = +/- $\"sqrt%2861%2F3%29\"$
\n" ); document.write( "subtract 4 from both sides, we have two solutions
\n" ); document.write( "t = -4 + $\"sqrt%2861%2F3%29\"$
\n" ); document.write( "and
\n" ); document.write( "t = -4 - $\"sqrt%2861%2F3%29\"$
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\n" ); document.write( "2.) 4s^2+s+2
\n" ); document.write( "Divide each term by 4 to make the coefficient of s^2 = 1, results
\n" ); document.write( "s^2 + $\"1%2F4\"$ s + $\"2%2F4\"$ = 0
\n" ); document.write( "s^2 + $\"1%2F4\"$ s + ___ = - $\"2%2F4\"$
\n" ); document.write( "Complete the square, half of (1/4) = (1/8); (1/8)^2 = (1/64)
\n" ); document.write( "s^2 + $\"1%2F4\"$ s + $\"1%2F64\"$ = - $\"2%2F4\"$ + $\"1%2F64\"$
\n" ); document.write( "s^2 + $\"1%2F4\"$ s + $\"1%2F64\"$ = - $\"32%2F64\"$ + $\"1%2F64\"$
\n" ); document.write( "s^2 + $\"1%2F4\"$ s + $\"1%2F64\"$ = - $\"31%2F64\"$
\n" ); document.write( "(s + $\"1%2F8\"$ )^2 = - $\"31%2F64\"$
\n" ); document.write( "s + $\"1%2F8\"$ = +/- $\"sqrt%28-31%2F64%29\"$
\n" ); document.write( "s = - $\"1%2F8\"$ +/- $\"sqrt%28-31%2F64%29\"$
\n" ); document.write( "Extract square root of -1 and square root of (1/64)
\n" ); document.write( "s = - $\"1%2F8\"$ +/- $\"1%2F8\"$ i $\"sqrt%2831%29\"$
\n" ); document.write( "Can also be written
\n" ); document.write( "s = $\"%28-1+%2B+sqrt%2831%29i%29%2F8\"$
\n" ); document.write( "and
\n" ); document.write( "s = $\"%28-1+-+sqrt%2831%29i%29%2F8\"$
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\n" ); document.write( "Was this sufficient steps?\r
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