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AnnZ [28]
2 years ago
5

Find x step by step (10 points)

Mathematics
2 answers:
zhannawk [14.2K]2 years ago
8 0
<h2><u>Answer:</u></h2>

\boxed{\left \{ {{\sqrt{(n-m)(m+n)}} \atop {-\sqrt{(n-m)(m+n)}}} \right.}

<h2><u>Solution Steps:</u></h2><h3><em>- Steps using the quadratic formula - </em></h3>

______________________________

<h3>1.)  <u>Subtract n² from both sides:</u></h3>
  • n^2-n^2=0
  • m^2-n^2=m^2-n^2

<h3>2.) <u>Rewrite:</u></h3>

<em>This equation is in standard form: ax² + bx² + c = 0. Substitute 1 for a, 0 for b, and (m-n) (m+n) for c in the quadratic formula, </em>\frac{-b\frac{+}{}\sqrt{b^2-4ac}  }{2a}:

  • x^2+m^2-n^2=0

<em>    </em>2.a)  <u>Turns into:</u>

  • x=\frac{0\frac{+}{}\sqrt{0^2-4(m-n)(m+n)}}{2}

<h3>3.) <u>Square 0:</u></h3>
  • 0^2=0 <em>(Also means it Cancels out.)</em>

<h3>4.)  <u>Take the square root of −4(m−n)(m+n):</u></h3>

<em>This just means combine them by squaring. </em>

  • -4^2=2<em> (Half it, don't square it.)</em>
  • (m-n)(m+n)^2=(n^2-m^2)

<em>    </em>4a.)<em>  </em><u>Our equation should look like this now:</u>

  • x=\frac{0\frac{+}{}2\sqrt{(n^2-m^2)}}{2}

<h3><u>5.)  </u><u>Solve the equation using </u><u>±</u><u>:</u></h3>

<em>Solve the equation </em>x=\frac{0\frac{+}{}2\sqrt{(n^2-m^2)}}{2}<em>:</em>

<em>    </em>5a.) <em> </em><u><em>Solve the equation when </em></u><u><em>± </em></u><u><em>is plus:</em></u>

  • x=\sqrt{(n-m)(m+n)}

   5b.) <em> </em><u><em>Solve the equation when </em></u><u><em>± </em></u><u><em>is minus:</em></u>

  • x=-\sqrt{(n-m)(m+n)}

______________________________

Hope this helps!

If you have any questions, or need help with anything else, feel free to ask! I'm happy to help!

- TotallyNotTrillex -

AleksandrR [38]2 years ago
4 0

Answer:

\sqrt{(n-m)(n+m)} & -\sqrt{(n-m)(n+m)}

Step-by-step explanation:

1) Subtract m^{2} from both sides. This should leave you with x^{2}=n^{2}-m^{2}.

2) Square root both sides. This should leave you with x=\sqrt{n^2-m^2} & x=-\sqrt{n^2-m^2}.

<em>You can stop here if this is what the problem is asking for. However, it is not fully simplified.</em>

<em />

3) Factor the equation. This should leave you with \sqrt{(n-m)(n+m)} & -\sqrt{(n-m)(n+m)}.

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