document.write( "Question 97800: How do you solve x to the second power-5x-6=0? \n" ); document.write( "
Algebra.Com's Answer #71155 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given:
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\n" ); document.write( "\"x%5E2+-+5x+-+6+=+0\"
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\n" ); document.write( "There are at least three ways you could solve this. You could graph the equation:
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\n" ); document.write( "\"y+=+x%5E2+-+5x+-6\"
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\n" ); document.write( "and find the values on the x axis where the graph crosses. Since a point on the x-axis has a
\n" ); document.write( "corresponding y-value of zero, wherever the graph crosses is the value of x that will make
\n" ); document.write( "the given equation equal to zero.
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\n" ); document.write( "You could use a method called \"completing the square\" or another equivalent way of doing this
\n" ); document.write( "method called the \"quadratic formula.\" If you haven't learned about the quadratic
\n" ); document.write( "equation (which is based on completing the square), you will.
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\n" ); document.write( "But in this problem, the easiest way to do it is by factoring. If you factor the left side
\n" ); document.write( "of the given equation you get:
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\n" ); document.write( "\"%28x+-+6%29%28x+%2B+1%29+=+0\"
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\n" ); document.write( "[You can multiply these two factors together and the answer will be \"x%5E2+-5x-6\" so
\n" ); document.write( "that the product of the factors is an equivalent replacement for the left side of the given
\n" ); document.write( "equation.]
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\n" ); document.write( "But notice if either of the factors equals zero, the multiplication of that zero times the
\n" ); document.write( "other factor results in zero as the answer. Therefore, if either factor is zero, the left
\n" ); document.write( "side of the equation will equal the zero on the right side of the equation.
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\n" ); document.write( "So now all you have to do is to find the value of x that makes each factor equal to zero. You
\n" ); document.write( "do that by setting the two factors (one at a time) equal to zero.
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\n" ); document.write( "\"x+-+6+=+0\"
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\n" ); document.write( "Solve for x by adding +6 to both sides to cancel out the -6 on the left side. When you
\n" ); document.write( "add +6 to both sides the result is:
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\n" ); document.write( "\"x+=+6\"
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\n" ); document.write( "Now set the other factor equal to zero:
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\n" ); document.write( "\"x+%2B+1+=+0\"
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\n" ); document.write( "Solve for x by getting rid of the +1 on the left side. Do this by subtracting 1 from both
\n" ); document.write( "sides and you end up with:
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\n" ); document.write( "\"x+=+-1\"
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\n" ); document.write( "So you have the two answers to your problem. The answers are x = 6 and x = -1.
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\n" ); document.write( "If you go back to the original problem of:
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\n" ); document.write( "\"x%5E2+-+5x+-+6+=+0\"
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\n" ); document.write( "and let x = 6 you get: \"6%5E2+-+5%2A6+-+6+=+36+-+30+-+6+=+0\" and this is what the left
\n" ); document.write( "side is supposed to be when x = 6.
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\n" ); document.write( "and if you let x = -1 you get \"%28-1%29%5E2+-+5%2A%28-1%29+-+6+=+1+%2B+5+-+6+=+0\" and this checks our
\n" ); document.write( "second answer of x = -1. For both these values of x, the left side of the given equation
\n" ); document.write( "becomes zero and therefore equals the right side.
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\n" ); document.write( "Hope this helps you to understand the problem and the ways you can use to solve it.
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