document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=560290>Question 560290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 64k^2+112k+49=0 I've tried several times to solve this equation. Would you please solve it and I'll practice others. Thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363812 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to solve:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64k%5E2%2B112k%2B49=0 ALIGN=MIDDLE  ALT=\"64k%5E2%2B112k%2B49=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation is in the standard quadratic equation form of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ak%5E2+%2B+b%2Ak+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"a%2Ak%5E2+%2B+b%2Ak+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and by comparing terms, we can see that a (the multiplier of the k-squared term) is +64, b (the multiplier of the k term) is +112, and c (the constant) is +49.<BR>\n" );
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document.write( "The quadratic formula says that if you have an equation of the standard quadratic form, the answer for k is given by:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For this problem, we identified the values for a as +64, b as +112, and c as +49. So we substitute those values into the equation for k to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%28-112+%2B-+sqrt%28+112%5E2-4%2A64%2A49+%29%29%2F%282%2A64%29+ ALIGN=MIDDLE  ALT=\"k+=+%28-112+%2B-+sqrt%28+112%5E2-4%2A64%2A49+%29%29%2F%282%2A64%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Inside the radical sign the 112 squared equals 12544 and the -4*64*49 equals -12544. Then in the denominator 2 * 64 = 128. When these values are substituted into the equation for k, the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%28-112+%2B-+sqrt%28+12544+-+12544+%29%29%2F%28128%29+ ALIGN=MIDDLE  ALT=\"k+=+%28-112+%2B-+sqrt%28+12544+-+12544+%29%29%2F%28128%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the terms inside the radical result in it becoming zero. So the equation for k is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-112%2F128 ALIGN=MIDDLE  ALT=\"k+=+-112%2F128\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the numerator and denominator are both even numbers, they are both divisible by some power of 2. For openers, let's try reducing them by dividing both by 8 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-14%2F16 ALIGN=MIDDLE  ALT=\"k+=+-14%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and both the numerator and denominator are again even numbers. Dividing them both by 2 gives the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-7%2F8 ALIGN=MIDDLE  ALT=\"k+=+-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can check this answer by returning to the equation that was given originally in the problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64k%5E2+%2B+112k+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"64k%5E2+%2B+112k+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F8 ALIGN=MIDDLE  ALT=\"-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > for k as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2A%28-7%2F8%29%5E2+%2B+112%2A%28-7%2F8%29+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"64%2A%28-7%2F8%29%5E2+%2B+112%2A%28-7%2F8%29+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "squaring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F8 ALIGN=MIDDLE  ALT=\"-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2F64 ALIGN=MIDDLE  ALT=\"49%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substituting this gives:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2A49%2F64+%2B+112%2A%28-7%2F8%29+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"64%2A49%2F64+%2B+112%2A%28-7%2F8%29+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel the 64 in the numerator and denominator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2864%29%2A49%2Fcross%2864%29+%2B+112%2A%28-7%2F8%29+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"cross%2864%29%2A49%2Fcross%2864%29+%2B+112%2A%28-7%2F8%29+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This reduces the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49+%2B+112%2A%28-7%2F8%29+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"49+%2B+112%2A%28-7%2F8%29+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the two terms of 49 and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98+%2B+112%2A%28-7%2F8%29+=+0 ALIGN=MIDDLE  ALT=\"98+%2B+112%2A%28-7%2F8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice in the second term the denominator 8 divides exactly into 112 to give 14. So the equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98+%2B+14%2A%28-7%29+=+0 ALIGN=MIDDLE  ALT=\"98+%2B+14%2A%28-7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and 14 times -7 is -98 which makes the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98+-+98+=+0 ALIGN=MIDDLE  ALT=\"98+-+98+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is obviously true, so the answer of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-7%2F8 ALIGN=MIDDLE  ALT=\"k+=+-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > checks and is, therefore, a correct answer.<BR>\n" );
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document.write( "I hope this helps you over the rough spot where you encountered difficulty with this problem.<BR>\n" );
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