You can put this solution on YOUR website!
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First multiply out the left side of the equation using the FOIL method (multiply First terms,
then Outside terms, then Inside terms, and then Last terms) and then collect like terms.
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The FOIL multiplication of the left side results in:
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The multiplications on the left side result in:
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Collect the like terms on the left side and you have:
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Subtract 7x from both sides to get:
.
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Finally add +1 to both sides and you get the standard form of:
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The left side of this equation can be factored. Since the 3 can only factor to 3*1 and also
since the -5 can only factor into 5*1 (without knowing whether the 5 or the 1 has the
minus sign) ... the factors are either:
. or:
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with the signs still to be added within each set of parentheses.
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The middle term of the quadratic polynomial is multiplied by -14. Therefore the cross products
must combine to be -14. Looks like the last group of factors is capable of producing that
result. The 3x times -5 would give -15x and the x times +1 would give +x. And the -15x and
the +x would combine to give us - 14x. Therefore we can write the factored equation as:
.
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Notice that this equation would be true if either of the multiplied factors on the left
side was equal to zero.
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One at a time set the two factors equal to zero to find the values of x that will satisfy
the equation.
. <--- subtract 1 from both sides to eliminate the +1 on the left.
. <--- divide both sides by +3, the multiplier of x
. <--- one value of x that satisfies the equation.
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Then for the second factor:
. <--- add 5 to both sides to eliminate the -5 on the left side.
. <--- the second value of x that satisfies the equation.
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Hope this gives you a little more insight into factoring in general and also in solving
a quadratic equation if factoring the polynomial is possible.
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