document.write( "Question 729502: I have a question about quadratic equation. I know if you need to square a negative number then it will be that number with an I at the end but we haven't learned that yet so I'm not sure if I'm doing the problem right. Here's what I'm doing:
\n" ); document.write( "4x^2-6x+2=0
\n" ); document.write( "6 plus or minus square root of (-6^2-4(4)(2)over 2(4)
\n" ); document.write( "6 plus or minus square root of (-36-72) over 8
\n" ); document.write( "6 plus of minus square root of (-108) over 8
\n" ); document.write( "Can you tell me what I am doing wrong? Or would the problem be considered non solvable? \n" ); document.write( "

Algebra.Com's Answer #445965 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
You tried to use
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ ,
\n" ); document.write( "the quadratic formula.
\n" ); document.write( "That cumbersome formula always works, but I only use it if I have to.
\n" ); document.write( "When you apply it properly, you get
\n" ); document.write( " $\"x+=+%28-%28-6%29+%2B-+sqrt%28%28-6%29%5E2-4%2A4%2A2+%29%29%2F%282%2A4%29+\"$ , which simplifies to
\n" ); document.write( " $\"x+=+%286+%2B-+sqrt%2836-32+%29%29%2F8+\"$
\n" ); document.write( "You had two errors:
\n" ); document.write( " $\"%28-6%29%5E2=%28-6%29%28-6%29=36\"$ Products of two negative numbers are positive, so all squares are always positive
\n" ); document.write( " $\"4%2A4%2A2=16%2A2=32\"$ I really do not know where your 72 came from.
\n" ); document.write( "So,
\n" ); document.write( " $\"x+=+%286+%2B-+sqrt%2836-32+%29%29%2F8+\"$ --> $\"x+=+%286+%2B-+sqrt%284%29%29%2F8+\"$ --> $\"x+=+%286+%2B-+2%29%2F8+\"$
\n" ); document.write( "That gives you solutions
\n" ); document.write( " $\"x=%286-2%29%2F8=4%2F8=1%2F2\"$ and $\"x=%286%2B2%29%2F8=8%2F8=1\"$ .
\n" ); document.write( "
\n" ); document.write( "NOTES:
\n" ); document.write( "Alternate ways to solve the problem are factoring, and completing the square.
\n" ); document.write( "You could have chosen to simplify the problem first and solve it by factoring, as ankor showed you better than what I was typing.
\n" ); document.write( "Factoring does not always work, and completing the square is not always easy.
\n" ); document.write( "However, the alternate ways do not require to memorize a formula, and sometimes they are much easier than applying the quadratic formula.
\n" ); document.write( "
\n" ); document.write( "Factoring:
\n" ); document.write( "I had typed my wordy explanation, but ankor did it better.
\n" ); document.write( "
\n" ); document.write( "Completing the square:
\n" ); document.write( " $\"%282x-3%2F2%29%5E2=%282x%29%5E2-2%282x%29%283%2F2%29%2B%283%2F2%29%5E2=4x%5E2-3x%2B9%2F4\"$ shares all the same terms in x as $\"4x%5E2-6x%2B2\"$
\n" ); document.write( " $\"4x%5E2-6x%2B2=0\"$ --> $\"4x%5E2-6x=-2\"$
\n" ); document.write( "Adding $\"9%2F16\"$ to both sides of the equal sign, we get a \"completed\" square on the left side:
\n" ); document.write( " $\"4x%5E2-6x%2B9%2F16=-2%2B9%2F4\"$ --> $\"4x%5E2-6x%2B9%2F16=1%2F4\"$ --> $\"%282x-3%2F2%29%5E2=1%2F4\"$
\n" ); document.write( "Since $\"%281%2F2%29%5E2=1%2F4\"$ and $\"%28-1%2F2%29%5E2=1%2F4\"$ it could be that
\n" ); document.write( " $\"2x-3%2F2=1%2F2\"$ or that $\"2x-3%2F2=-1%2F2\"$ and each of those equations leads us to a solution. \n" ); document.write( "

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