Question

Find x step by step (10 points)

Answer 1

Answer:

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

Solution Steps:

- Steps using the quadratic formula -

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1.)  Subtract n² from both sides:

• $n^2-n^2=0$

• $m^2-n^2=m^2-n^2$

2.) Rewrite:

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, $\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}$:

• $x^2+m^2-n^2=0$

   2.a)  Turns into:

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

3.) Square 0:

• $0^2=0$ (Also means it Cancels out.)

4.)  Take the square root of −4(m−n)(m+n):

This just means combine them by squaring.

• $-4^2=2$ (Half it, don't square it.)

• $(m-n)(m+n)^2=(n^2-m^2)$

   4a.)  Our equation should look like this now:

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

5.)  Solve the equation using ±:

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

   5a.) Solve the equation when ± is plus:

• $x=\sqrt{(n-m)(m+n)}$

   5b.) Solve the equation when ± is minus:

• $x=-\sqrt{(n-m)(m+n)}$

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Hope this helps!

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

- TotallyNotTrillex -

Answer 2

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 $x=\sqrt{n^2-m^2}$ & $x=-\sqrt{n^2-m^2}$.

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

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