document.write( "Question 621573: Please help me solve the equation 8x^2+28=36 I need to factor for the larger and smaller values. I would appreciate if I could get all steps involved. \n" ); document.write( "

Algebra.Com's Answer #390829 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"8x%5E2%2B28=36\"$ --> $\"8x%5E2%2B28-28=36-28\"$ --> $\"8x%5E2=8\"$ --> $\"8x%5E2%2F8=8%2F8\"$ --> $\"x%5E2=1\"$ --> $\"highlight%28x=1%29\"$ or $\"highlight%28x=-1%29\"$
\n" ); document.write( "But I suspect you may have a typo and the problem was a bit more complicated.
\n" ); document.write( "In general you would first have a polynomial on the left side equal to zero on the right side.
\n" ); document.write( "For example:
\n" ); document.write( " $\"8x%5E2%2B28x=36\"$ --> $\"8x%5E2%2B28x-36=36-36\"$ --> $\"8x%5E2%2B28x-36=0\"$
\n" ); document.write( "Next you would look for factors that are common to all the terms, as in
\n" ); document.write( " $\"8x%5E2%2B28x-36=0\"$ --> $\"4%2A%282x%5E2%29%2B4%2A%287x%29%2B4%2A%28-9%29=0\"$ --> $\"4%2A%282x%5E2%2B7x-9%29=0\"$
\n" ); document.write( "In that case, since 4 is not zero the other factor must be zero, so you would be looking for solutions to
\n" ); document.write( " $\"2x%5E2%2B7x-9=0\"$
\n" ); document.write( "The next step in factoring quadratic trinomials like $\"2x%5E2%2B7x-9=0\"$ is \"deconstructing\" the product of the two factors.
\n" ); document.write( "The product initially has one term in $\"x%5E2\"$ , one independent term (with no x) and two terms in $\"x\"$ that are later joined by \"collecting like terms.\"
\n" ); document.write( "Factoring is simpler when there is no coefficient in front of the $\"x%5E2\"$ .
\n" ); document.write( "If there is one, you first multiply it times the independent term (the term without x).
\n" ); document.write( "In this case you get $\"2%28-9%29=-18\"$ , but do not worry much about the sign, just think of 18 for now.
\n" ); document.write( "You look for pairs of factors that multiply to yield that number, and list them all.
\n" ); document.write( "In this case there are only 3 pairs:
\n" ); document.write( " $\"18=1%2A18\"$
\n" ); document.write( " $\"18=2%2A9\"$
\n" ); document.write( " $\"18=3%2A6\"$
\n" ); document.write( "From the negative sign of the independent term (-9) you know that there is a factor with a negative sign and one with a positive sign, which will ultimately give rise to the term $\"7x\"$ with a positive sign.
\n" ); document.write( "You look for a pair of factors from the listing above that will add to 7 when given opposite signs.
\n" ); document.write( "The answer is 9-2=7.
\n" ); document.write( "So the deconstructed product will be
\n" ); document.write( " $\"2x%5E2%2B9x-2x-9\"$
\n" ); document.write( "Grouping the terms in pairs and taking out common factors comes next
\n" ); document.write( " $\"2x%5E2%2B9x-2x-9=%282x%5E2-2x%29%2B%289x-9%29=2x%28x-1%29%2B9%28x-1%29=%282x%2B9%29%28x-1%29\"$
\n" ); document.write( "After finding the factors, solving the equation is easy
\n" ); document.write( "The whole solution can be summarized as
\n" ); document.write( " $\"8x%5E2%2B28x=36\"$ --> $\"8x%5E2%2B28x-36=0\"$ --> $\"2x%5E2%2B7x-9=0\"$ --> $\"%282x%2B9%29%28x-1%29=0\"$ --> $\"2x%2B9=0\"$ or $\"x-1=0\"$
\n" ); document.write( "There are two solutions:
\n" ); document.write( " $\"2x%2B9=0\"$ --> $\"2x=-9\"$ --> $\"highlight%28x=-9%2F2%29\"$ and
\n" ); document.write( " $\"x-1=0\"$ --> $\"highlight%28x=1%29\"$
\n" ); document.write( " \n" ); document.write( "

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