document.write( "Question 60107: How do you complete the square of x2-8x=33 and x2-8x+40=0 \n" ); document.write( "
Algebra.Com's Answer #41449 by ankor@dixie-net.com(22740)\"\" \"About 
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Complete the square by filling in the blank to make it a perfect square:
\n" ); document.write( "x^2 - 8x + ___ = 33
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\n" ); document.write( "Take the coefficient of x, divide it by 2 and square it:
\n" ); document.write( "Coefficient is -8, divided by 2 is -4, squaring 4 gives you + 16
\n" ); document.write( "Remember if you add 16 to the left side of the equation you must do the same to the right side.
\n" ); document.write( "x^2 - 8x + 16 = 33 + 16
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\n" ); document.write( "x^2 - 8x + 16 = 49
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\n" ); document.write( "Since we made it a perfect square we can write it:
\n" ); document.write( "(x - 4)^2 = 49
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\n" ); document.write( "Find the square root of both sides:
\n" ); document.write( "(x - 4) = +/-7
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\n" ); document.write( "x = +4 + 7
\n" ); document.write( "x = +11
\n" ); document.write( "and
\n" ); document.write( "x = +4 - 7
\n" ); document.write( "x = -3
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\n" ); document.write( "The solution is x = +11 and x = -3
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\n" ); document.write( "x^2 - 8x + 40 = 0
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\n" ); document.write( "Subtract 40 from both sides and complete the square:
\n" ); document.write( "x^2 - 8x + ___ = -40
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\n" ); document.write( "Since the coefficient of x is 8 again. we will have:
\n" ); document.write( "x^2 - 8x + 16 = -40 + 16
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\n" ); document.write( "x^2 - 8x + 16 = -24
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\n" ); document.write( "(x -4)^2 = - 24
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\n" ); document.write( "x - 4 = +/-SqRt(-24)
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\n" ); document.write( "Using the i factor (which is the square root of -1)
\n" ); document.write( "x - 4 = +/- i*SqRt(+24)
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\n" ); document.write( "x - 4 = +/- i*SqRt(4*6)
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\n" ); document.write( "Extract 2 by taking out the square root of 4
\n" ); document.write( "x - 4 = +/- 2i*SqRt(6)
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\n" ); document.write( "x = 4 + 2i*SqRt(6)
\n" ); document.write( "and
\n" ); document.write( "x = 4 - 2i*SqRt(6)
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\n" ); document.write( "Did this make sense to you??
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