# Finding Min Value: 2x^2-36x+175

• Taylor_1989
In summary, the conversation discusses the process of completing the square for the expression 2x^2-36x+175. The person asking the question is confused about the correct method to use and is seeking clarification. They later realize their mistake and provide the correct solution. The conversation also mentions using differentiation to check the answer.
Taylor_1989
Right so, I actually know the math, my problem is that I think, I am getting confused with wording. I will explain better where I show you where my problem lies.

Question: Show that $2x^2-36x+175$ mat be written in $a(x-b)+c$ where the values a,b,c are to be found.

state, with reason, the least possible value of $2x^2-36x+175$

so basically I complete the square, I get $2(x-9)+26$ the book ans $1(x-9)+13$ so all they have done is not multiplied back through by 2.

The when it comes to find the least possible value x=9 and y= 13. I did check this with differentiation and get x=9 which don't get me wrong I can see that, but what I don't understand, my books when ever completing the square always multiply through with the number factored out. This has cause some confusion on my part.

Taylor_1989 said:
Right so, I actually know the math, my problem is that I think, I am getting confused with wording. I will explain better where I show you where my problem lies.

Question: Show that $2x^2-36x+175$ mat be written in $a(x-b)+c$ where the values a,b,c are to be found.
That would have to be a(x - b)2 + c, which is not what you wrote. You are consistently omitting this exponent, so it doesn't seem to be merely a typo.
Taylor_1989 said:
state, with reason, the least possible value of $2x^2-36x+175$

so basically I complete the square, I get $2(x-9)+26$ the book ans $1(x-9)+13$ so all they have done is not multiplied back through by 2.
Both answers are incorrect, which can be seen if you expand each expression. Neither one expands to 2x2 - 36x + 175.

Taylor_1989 said:
The when it comes to find the least possible value x=9 and y= 13. I did check this with differentiation and get x=9 which don't get me wrong I can see that, but what I don't understand, my books when ever completing the square always multiply through with the number factored out. This has cause some confusion on my part.

Nope it was a typo, I was doing quickly on a break, did not have a lot of time, so rushed through, still no excuses; apologise on my behalf . Here is how I worked it out: $2x^2-36x+175 \rightarrow 2(x^2-18x+\frac{175}{2}) \rightarrow 2((x-9)^2+\frac{175}{2}-\frac{162}{2}) \rightarrow 2((x-9)^2+\frac{13}{2}) \rightarrow 2(x-9)^2+13$

which I believe is correct??

I did multiply back through and got the correct ans.

I do actual think I have ans my own question in doing this, but wouldn't mind the input.

Once again I do apologise for my pervious mistake, I do not wish to think I was wasting your time.

Taylor_1989 said:
Nope it was a typo, I was doing quickly on a break, did not have a lot of time, so rushed through, still no excuses; apologise on my behalf . Here is how I worked it out: $2x^2-36x+175 \rightarrow 2(x^2-18x+\frac{175}{2}) \rightarrow 2((x-9)^2+\frac{175}{2}-\frac{162}{2}) \rightarrow 2((x-9)^2+\frac{13}{2}) \rightarrow 2(x-9)^2+13$

which I believe is correct??
Yes, this is correct. The only change I would make is to use = between each pair of expressions instead of an arrow.
Taylor_1989 said:
I did multiply back through and got the correct ans.

I do actual think I have ans my own question in doing this, but wouldn't mind the input.

Once again I do apologise for my pervious mistake, I do not wish to think I was wasting your time.

## 1. What is the equation for finding the minimum value of 2x^2-36x+175?

The equation for finding the minimum value of 2x^2-36x+175 is y = 2x^2-36x+175.

## 2. How do you find the minimum value of 2x^2-36x+175?

To find the minimum value of 2x^2-36x+175, you can use the formula x = -b/2a, where a and b are the coefficients of the x^2 and x terms in the equation, respectively. Plug this value of x into the original equation to find the minimum value of y.

## 3. Can the minimum value of 2x^2-36x+175 be negative?

Yes, the minimum value of 2x^2-36x+175 can be negative. This will occur when the value of x that minimizes the equation is a negative number.

## 4. What is the minimum value of 2x^2-36x+175?

The minimum value of 2x^2-36x+175 depends on the value of x that minimizes the equation. To find the exact minimum value, you will need to solve for the value of x using the formula x = -b/2a and plug this value into the original equation to find the minimum value of y.

## 5. How can finding the minimum value of 2x^2-36x+175 be useful in real-life applications?

Finding the minimum value of 2x^2-36x+175 can be useful in real-life applications when trying to optimize a certain variable. For example, if the equation represents the cost of producing a product, finding the minimum value can help determine the most cost-efficient production level. Additionally, finding the minimum value can also be useful in finding the minimum or maximum points of a curve in physics or engineering problems.

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