how would I solve x^2 = 4x + 5 (from exponential eqn)

B

Brad

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How would I solve this please? x . x = 4x + 5 ?, that's x squared = 4x+5

The assignment is solve the equations and the original equation was

e (constant) to the x squared is = e (constant) 4x + 5 and I was taught that I can eliminate my bases when they are the same, so the equation would become x squared = 4x +5. Mathematically I know my answers are 5 and -1, but I am not sure what the next step algebraically is to come to those answers.

I tried with 4x+5-x squared=0, but that didn't seem to work. Neither did subtracting 5 from either side.
 
Re: Intermediate algebra



Hello Brad:

There are many ways to solve this equation.

One foolproof way is to rearrange it so that you can identify the values of a, b, and c (i.e., the coefficients in a quadratic polynomial), followed by using the quadratic formula to find the values of x which cause that polynomial to evaluate to zero.

Here is my boilerplate response, for you, as well.

At the top of this board's index, you will find a post titled, "Read Before Posting".

Please, read it.

It outlines your responsibilities for seeking help at this web site.

The main points of that post are (1) those of us who regularily provide help at this site do not simply guess at which lessons we could type for you to provide solutions for your homework, and (2) you make it very difficult for people to help you when you withhold your existing knowledge and attempts.

After you read your responsibilities, then please come back and show us what you've been able to accomplish so far on this exercise. It would be even better if you could also include statements about why you're stuck.

Once you clue me in as to what you already know, then I am eager to guide you.

Cheers,

~ Mark :)



"Spoon feeding, in the long run, teaches us nothing but the shape of the spoon" -- E.M. Forster

"It is a waste of my personal time to type a bunch of stuff that people already know." -- Yours Truly

 
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Re: Intermediate algebra

Where is "read before posting" tab?
 
Re: Intermediate algebra

The assignment is solve the equations and the original equation was

e (constant) to the x squared is = e (constant) 4x + 5 and I was taught that I can eliminate my bases when they are the same, so the equation would become x squared = 4x +5. Mathematically I know my answers are 5 and -1, but I am not sure what the next step algebraically is to come to those answers.
 
Re: Intermediate algebra

Brad said:
The assignment is solve the equations and the original equation [is]

e (constant) to the x squared is = e (constant) [to the (4x + 5)]

and I was taught that I can eliminate my bases when they are the same, so the equation would become x squared = 4x +5.
Click to expand...


I read the equation as follows.

\(\displaystyle e^{x^2} \;=\; e^{4x + 5}\)

Yup, anytime two powers of (any) equal base are equal, the exponents must also be equal.
Mathematically I know my answers are 5 and -1, but I am not sure what the next step algebraically is to come to those answers.
Click to expand...


How do you mathematically know these solutions? (For this question, I would like to see your answer.)

Hold on, while I search for a link on how to solve quadratic equations in the form of a*x^2 + b*x + c = 0 ...

~ Mark :)

 
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