document.write( "Question 779265: Find all real solutions of the equation\r
\n" ); document.write( "\n" ); document.write( "x-7sqrt(x) +10=0\r
\n" ); document.write( "\n" ); document.write( "10 is not in the sqrt\r
\n" ); document.write( "\n" ); document.write( "what steps must I first take to get rid of the square root \n" ); document.write( "

Algebra.Com's Answer #475183 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
The solution provided by another tutor is perfectly correct. But the \"what steps ... get rid of the square root\" in your post suggests that this other solution does not use the method you may be learning in school.

\n" ); document.write( "To eliminate a square root:

Isolate that square root term on one side of the equation.
Square both sides

\n" ); document.write( " $\"x-7sqrt%28x%29%2B10=0\"$
\n" ); document.write( "Adding the square root term we get:
\n" ); document.write( " $\"x%2B10=7sqrt%28x%29\"$
\n" ); document.write( "(The square root term is sufficiently isolated. If the 7 in front bothers you, then you can divide both sides by 7.) Squaring both sides:
\n" ); document.write( " $\"%28x%2B10%29%5E2=%287sqrt%28x%29%29%5E2\"$
\n" ); document.write( " $\"x%5E2%2B20x%2B100=49x\"$

\n" ); document.write( "With the square root eliminated we can now solve the resulting equation. This is quadratic so we want a zero on one side. Subtracting 49x from each side we get:
\n" ); document.write( " $\"x%5E2-29x%2B100=0\"$
\n" ); document.write( "Factoring:
\n" ); document.write( " $\"%28x-25%29%28x-4%29=0\"$
\n" ); document.write( "From the Zero Product Property:
\n" ); document.write( "x-25 = 0 or x-4 = 0
\n" ); document.write( "which give us:
\n" ); document.write( "x = 25 or x = 4

\n" ); document.write( "And just as the other tutor said, we must check our solutions. Both of them work so they are both solutions to the original equation.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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