Substitution Method

[SPIRITWARRIOR]

Solve the following equation using the substitution method.
x^4 –5x^2 –14=0
Complete the following steps to solve the above equation:
Let u=x^2, substitute the variables, and write the new equation.
Now factor the new equation, apply the zero-product principle, and solve for u.
Now substitute u=x^2 to solve for x.


I have several questions like this but would like it if someone could help me with this problem in particular and show me step by step the process.

Thanks,
Sara

 

[Ted]

Huh. It sure does. I wonder what's going on.....

 

[daon2]

^ As does yours Denis

Huh. It sure does. I wonder what's going on.....

but not yours

edit: test
[Ted, this one gives blank screen if "reply with quote" is attempted]


> x^4 –5x^2 –14=0
> Complete the following steps to solve the above equation:
> Let u=x^2, substitute the variables, and write the new equation.

What exactly is your question?
Do you understand that equation becomes: u^2 - 5u - 14 = 0?

 

[daon2]

Copying and pasting the text either using source formatting or removing the formatting (by first pasting in notepad, recopying and pasting) results in a blank box.

Probably either (a) An issue with your autolink script, or (b) a special character or two screwing with your server processing.

 

[Ted]

Copying and pasting the text either using source formatting or removing the formatting (by first pasting in notepad, recopying and pasting) results in a blank box.

Probably either (a) An issue with your autolink script, or (b) a special character or two screwing with your server processing.

Problem has been resolved. Whew.

 

[Deleted member 4993]

Solve the following equation using the substitution method.
x^4 –5x^2 –14=0
Complete the following steps to solve the above equation:
Let u=x^2, substitute the variables, and write the new equation.
Now factor the new equation, apply the zero-product principle, and solve for u.
Now substitute u=x^2 to solve for x.


I have several questions like this but would like it if someone could help me with this problem in particular and show me step by step the process.

Thanks,
Sara

I'll solve a similar but differnt problem.

solve

x⁴ - 13x² + 36 = 0

substitute

u = x²

then we get

u² - 13u + 36 = 0

using quadratic equation (or any other favorite method), we get

(u - 9) * (u - 4) = 0

back substitute u = x²

(x² - 3²)(x² - 2²) = 0

then

x = -3, +3, -2 & +2

 

[SPIRITWARRIOR]

Thank you, that was helpful!

I'll solve a similar but differnt problem.

solve

x⁴ - 13x² + 36 = 0

substitute

u = x²

then we get

u² - 13u + 36 = 0

using quadratic equation (or any other favorite method), we get

(u - 9) * (u - 4) = 0

back substitute u = x²

(x² - 3²)(x² - 2²) = 0

then

x = -3, +3, -2 & +2

 

[lookagain]

I'll solve a similar but differnt problem.

solve

x⁴ - 13x² + 36 = 0

\(\displaystyle \cdot\)

\(\displaystyle \cdot\)

\(\displaystyle \cdot\)

\(\displaystyle \cdot\)


x = -3, +3, -2 \(\displaystyle \ \) > > & < < \(\displaystyle \ \) +2

Be careful.


x = -3, +3, -2, or +2.