document.write( "Question 41521: Find all real solutions to the equation\r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28x%2B4%29-2sqrt%28x-1%29=-1%29\"$ \n" ); document.write( "

Algebra.Com's Answer #26791 by Nate(3500) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%28x%2B4%29-2sqrt%28x-1%29=-1%29\"$
\n" ); document.write( " $\"sqrt%28x%2B4%29+=+-1+%2B+2sqrt%28x-1%29\"$
\n" ); document.write( " $\"%28sqrt%28x%2B4%29%29%5E2+=+%28-1+%2B+2sqrt%28x-1%29%29%5E2\"$
\n" ); document.write( " $\"x+%2B+4+=+1+-+4sqrt%28x-1%29+%2B+4%28x-1%29\"$
\n" ); document.write( " $\"x+%2B+4+=+1+-+4sqrt%28x-1%29+%2B+4x+-+4\"$
\n" ); document.write( " $\"x+%2B+4+=+-4sqrt%28x-1%29+%2B+4x+-+3\"$
\n" ); document.write( " $\"-3x+%2B+7+=+-4sqrt%28x-1%29\"$
\n" ); document.write( " $\"%283%2F4%29x+-+%287%2F4%29+=+sqrt%28x-1%29\"$
\n" ); document.write( " $\"%28%283%2F4%29x+-+%287%2F4%29%29%5E2+=+%28sqrt%28x-1%29%29%5E2\"$
\n" ); document.write( " $\"%289%2F16%29x%5E2+-+%2842%2F16%29x+%2B+%2849%2F16%29+=+x+-+1\"$
\n" ); document.write( " $\"9x%5E2+-+42x+%2B+49+=+16x+-+16\"$
\n" ); document.write( " $\"9x%5E2+-+58x+%2B+65+=+0\"$
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"9x%5E2%2B-58x%2B65+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-58%29%5E2-4%2A9%2A65=1024\"$ .
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\n" ); document.write( " Discriminant d=1024 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--58%2B-sqrt%28+1024+%29%29%2F2%5Ca\"$ .
\n" ); document.write( "
\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-58%29%2Bsqrt%28+1024+%29%29%2F2%5C9+=+5\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-58%29-sqrt%28+1024+%29%29%2F2%5C9+=+1.44444444444444\"$
\n" ); document.write( "
\n" ); document.write( " Quadratic expression $\"9x%5E2%2B-58x%2B65\"$ can be factored:
\n" ); document.write( " $\"9x%5E2%2B-58x%2B65+=+9%28x-5%29%2A%28x-1.44444444444444%29\"$
\n" ); document.write( " Again, the answer is: 5, 1.44444444444444.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-58%2Ax%2B65+%29\"$

\n" ); document.write( "\n" ); document.write( " $\"x+=+5\"$ and $\"x+=+13%2F9\"$
\n" ); document.write( "Check:
\n" ); document.write( " $\"sqrt%28x%2B4%29-2sqrt%28x-1%29=-1%29\"$
\n" ); document.write( " $\"sqrt%285%2B4%29-2sqrt%285-1%29=-1%29\"$
\n" ); document.write( " $\"sqrt%289%29-2sqrt%284%29=-1%29\"$
\n" ); document.write( " $\"3-2%282%29=-1%29\"$
\n" ); document.write( " $\"3-4=-1%29\"$ Five Works
\n" ); document.write( "Check:
\n" ); document.write( " $\"sqrt%28x%2B4%29-2sqrt%28x-1%29=-1%29\"$
\n" ); document.write( " $\"sqrt%28%2813%2F9%29%2B4%29-2sqrt%28%2813%2F9%29-1%29=-1%29\"$
\n" ); document.write( " $\"sqrt%28%2813%2F9%29%2B%2836%2F9%29%29-2sqrt%28%2813%2F9%29-%289%2F9%29%29=-1%29\"$
\n" ); document.write( " $\"sqrt%2849%2F9%29-2sqrt%284%2F9%29=-1%29\"$
\n" ); document.write( " $\"%287%2F3%29-2%282%2F3%29=-1%29\"$
\n" ); document.write( " $\"%287%2F3%29-%284%2F3%29=-1%29\"$
\n" ); document.write( " $\"%283%2F3%29=-1%29\"$ (13/9) Does Not Work \n" ); document.write( "

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