i am having a minor difficulty
i've been stuck for over an hour and don't know what to do
i don't know is this right
? = "+" or "-"
# = number
y=3
(x-3)^2 + (y-4)^2 = 9
i substitute y
(x-3)^2 + (3-4)^2 = 9
(x-3)^2 + 1 = 9
x^2 - 6x + 9 + 1 = 9
x^2 - 6x + 10 = 9
x^2 - 6x + 1 = 0
(x ? #)(x ? #) = 0
i get to here and now i am stuck
can u correct me if i did something wrong
please and thank you
you are correct.
Use the quadratic formula
x= (-b+-sqrt (b^2-4ac))/2a
or do it this way:
(x-3)^1+1=9
(x-3)^2=8= 2*2^2
take the sqrt of each side
x-3=+-2*sqrt2
x= 3+sqrt2 or x=3-sqrt2
im confused
Check with your teacher, then.
It seems like you are trying to solve a quadratic equation. Let's walk through the steps together and see if we can identify any mistakes.
First, you correctly substituted the value of y into the equation. The next step you did was expanding and simplifying the equation:
(x-3)^2 + (3-4)^2 = 9
(x-3)^2 + 1 = 9
So far, so good. However, the mistake happened in the following step:
x^2 - 6x + 9 + 1 = 9
It seems like you made an error in expanding (x-3)^2. The correct expansion should be x^2 - 6x + 9. Let's fix that:
x^2 - 6x + 1 = 9
Now, to continue solving the equation, we need to isolate the terms with x on one side:
x^2 - 6x + 1 - 9 = 0
x^2 - 6x - 8 = 0
Now the equation is in the standard quadratic form, ax^2 + bx + c = 0. In this case, a = 1, b = -6, and c = -8.
To continue solving, you can use various methods such as factoring, completing the square, or using the quadratic formula. Since factoring may not be straightforward in this case, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values a = 1, b = -6, and c = -8 into the formula, we get:
x = (-(-6) ± √((-6)^2 - 4(1)(-8))) / (2(1))
x = (6 ± √(36 + 32)) / 2
x = (6 ± √68) / 2
x = (6 ± 2√17) / 2
x = 3 ± √17
Therefore, the solutions to the equation are x = 3 + √17 and x = 3 - √17.
To summarize, the corrected steps are:
1. Substitute y:
(x-3)^2 + (3-4)^2 = 9
(x-3)^2 + 1 = 9
2. Simplify the equation:
x^2 - 6x + 1 = 9
3. Rearrange the equation:
x^2 - 6x - 8 = 0
4. Solve using the quadratic formula:
x = (6 ± √68) / 2
x = 3 ± √17
I hope this clears up the confusion and helps you move forward with solving the equation. If you have any further questions, feel free to ask!