document.write( "Question 590370: Find the number k such that the given equation has exactly one real solution:\r
\n" ); document.write( "\n" ); document.write( "kx^2+28x+4=0\r
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Algebra.Com's Answer #375150 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
For $\"kx%5E2%2B28x%2B4+=+0\"$ to have exactly one real solution. the factors of this equation have to be equal.
\n" ); document.write( "For example $\"%28ax%2Bb%29%28ax%2Bb%29\"$ so that $\"b+=+2\"$ and $\"a+=+7\"$ to get:
\n" ); document.write( " $\"7x%2B2%29%287x%2B2%29+=+49x%5E2%2B28x%2B4\"$ and the solution(s) is(are) $\"x+=+-0.28571434\"$
\n" ); document.write( "So $\"k+=+49\"$
\n" ); document.write( "But you could do it this way:
\n" ); document.write( " $\"kx%5E2%2B28x%2B4+=+0\"$ Complete the square. First, divide by k.
\n" ); document.write( " $\"%28kx%5E2%2B28x%2B4%29%2F%28k%29%29\"$ = $\"0\"$ Simplify.
\n" ); document.write( " $\"x%5E2%2B28x%2Fk+%2B4%2Fk+=+0\"$ To complete the square, the constant term must equal the square of half the x-coefficient, so $\"%28%281%2F2%29%2828%2Fk%29%29%5E2+=+%2814%2Fk%29%5E2\"$ = $\"196%2Fk%5E2\"$
\n" ); document.write( "Set this equal to the constant term $\"4%2Fk\"$ and solve for k.
\n" ); document.write( " $\"196%2Fk%5E2+=+4%2Fk\"$ Simplify.
\n" ); document.write( " $\"196%2Fk+=+4\"$
\n" ); document.write( " $\"k+=+196%2F4\"$
\n" ); document.write( " $\"k+=+49\"$
\n" ); document.write( "So the equation is:
\n" ); document.write( " $\"49x%5E2%2B28x%2B4+=+0\"$
\n" ); document.write( " $\"graph%28400%2C400%2C-2%2C2%2C-5%2C5%2C49x%5E2%2B28x%2B4%29\"$ \r
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