document.write( "Question 196350: Hello.\r
\n" ); document.write( "\n" ); document.write( "I'm having some trouble with the following problem:\r
\n" ); document.write( "\n" ); document.write( "Find all values of k that ensure that the given equation has exactly one solution.
\n" ); document.write( "10x^2 + kx + 8 = 0 \n" ); document.write( "

Algebra.Com's Answer #147183 by RAY100(1637) $\"\"$ $\"About$

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10 x^2 +kx +8 =0
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\n" ); document.write( "divide by 10
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\n" ); document.write( "x^2 + (k/10)x + 8/10 =0
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\n" ); document.write( "To get one equal answer, we must have sums squared, (x+a) (x+a) =0,
\n" ); document.write( "To complete the square, the coefficient of the 2nd term is halved and then squared
\n" ); document.write( "to equal the third term
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\n" ); document.write( "(k/(2*10))^2 = 8/10
\n" ); document.write( "k^2/400 = 8/10
\n" ); document.write( "k^2 = 320
\n" ); document.write( "k= +/- 17.88,,,,(8sqrt5)
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\n" ); document.write( "checking
\n" ); document.write( "10 x^2 +(17.88)x +8 =0
\n" ); document.write( "x^2 +1.788 x +.8 =0
\n" ); document.write( "(x+sqrt.8)(x+sqrt.8) =0
\n" ); document.write( "(x +.894) (x+.894) =0
\n" ); document.write( "x= -.894, -.894,,, ok
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\n" ); document.write( "checking with k=-17.887,,,,,finds the same,, except x= +.894, +.894 ,,,ok \n" ); document.write( "

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