document.write( "Question 695470: So i wanted to solve this problem wicht is f(x)=x^2 + 7\r
\n" ); document.write( "\n" ); document.write( "Please i really need help \n" ); document.write( "

Algebra.Com's Answer #428508 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+f%28x%29+=+x%5E2+%2B+7+\"$
\n" ); document.write( "Can you read this OK?
\n" ); document.write( "It says: \" There is a function called $\"+f%28x%29+\"$ which
\n" ); document.write( "equals $\"+x%5E2+%2B+7+\"$ .
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\n" ); document.write( "You can plug in a value for $\"+x+\"$ on both sides like this:
\n" ); document.write( " $\"+f%282%29+=+2%5E2+%2B+7+\"$
\n" ); document.write( " $\"+f%282%29+=+4+%2B+7+\"$
\n" ); document.write( " $\"+f%282%29+=+11+\"$
\n" ); document.write( "-------------
\n" ); document.write( "When you say \" Solve the problem \" , I assume you want
\n" ); document.write( "to find the \"roots\" of the equation. The roots are any and
\n" ); document.write( "all values of $\"+x+\"$ for which $\"+f%28x%29+=+0+\"$
\n" ); document.write( "--------------
\n" ); document.write( " $\"+f%28x%29+=+0+\"$
\n" ); document.write( " $\"+x%5E2+%2B+7+=+0+\"$
\n" ); document.write( " $\"+x%5E2+=+-7+\"$
\n" ); document.write( "Do you understand imaginary numbers? You need to use the fact
\n" ); document.write( "that $\"+i+=+sqrt%28-1%29+\"$ .
\n" ); document.write( " $\"+x%5E2+=+-7+\"$
\n" ); document.write( " $\"+x%5E2+=+-1%2A7+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"+x+=+sqrt%28-1%29+%2A+sqrt%287%29+\"$
\n" ); document.write( "There are two square roots of $\"7\"$ . They are
\n" ); document.write( " $\"+sqrt%287%29+\"$ and $\"+-sqrt%287%29+\"$ , another answer is
\n" ); document.write( " $\"+x+=+sqrt%28-1%29+%2A+%28+-sqrt%287%29+%29+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "And, since $\"+i+=+sqrt%28-1%29+\"$ ,
\n" ); document.write( " $\"+x+=+sqrt%287%29%2Ai+\"$
\n" ); document.write( " $\"+x+=+-sqrt%287%29%2Ai+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "So, you have two imaginary solutions to
\n" ); document.write( " $\"+x%5E2+%2B+7+=+0+\"$
\n" ); document.write( "This is always the case when the plot of the
\n" ); document.write( "parabola ( which the function is ) does not
\n" ); document.write( "cross the x-axis.
\n" ); document.write( "-----------------
\n" ); document.write( "If the function $\"+f%28x%29+\"$ did cross the x-axis, then
\n" ); document.write( "the solutions would be:
\n" ); document.write( " $\"+x+\"$ = value of $\"x\"$ at one of the crossings
\n" ); document.write( " $\"+x+\"$ = value of $\"x\"$ at the other crossing
\n" ); document.write( "---------------------------------------
\n" ); document.write( "To demonstrate, here's two plots, $\"+f%28x%29+=+x%5E2+%2B+7+\"$
\n" ); document.write( "and a parabola which actually crosses the x-axis.
\n" ); document.write( "Your function floats above the x-axis, so it can't
\n" ); document.write( "have \"real\" roots. They must be \"imaginary\"
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-8%2C+8%2C+-20%2C+20%2C+x%5E2+%2B+7%2C+x%5E2+-+7+%29+\"$
\n" ); document.write( "Just keep learning how to talk about equations
\n" ); document.write( "before solving them. Them key is knowing exactly
\n" ); document.write( "what the words mean.
\n" ); document.write( "Good luck
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