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