Answer:
55 =x
Step-by-step explanation:
x+15=2x-40
Subtract x from each side
x-x+15=2x-x-40
15 = x-40
Add 40 to each side
15+40 = x-40+40
55 =x
20
...........................
The first equation above is exponential; the second one is a quadratic; the third one is a line with a y-intercept at the origin. Of those, the exponential one grows fastest.
Step-by-step explanation:
The quadratic formula is:
![x = \frac{-b \pm\sqrt{b^2-4ac} }{2a}\\](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D%5C%5C)
A, in this case, is -2.
B is 5
C is -11
x = ![\frac{-5 \pm\sqrt{5^2-4(-2)(-11)} }{2(-2)}](https://tex.z-dn.net/?f=%5Cfrac%7B-5%20%5Cpm%5Csqrt%7B5%5E2-4%28-2%29%28-11%29%7D%20%7D%7B2%28-2%29%7D)
x = ![\frac{-5\pm\sqrt{25 -88} }{-4}\\](https://tex.z-dn.net/?f=%5Cfrac%7B-5%5Cpm%5Csqrt%7B25%20-88%7D%20%7D%7B-4%7D%5C%5C)
x = ![\frac{-5\pm\sqrt{-63}}{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B-5%5Cpm%5Csqrt%7B-63%7D%7D%7B-4%7D)
x =
and ![\frac{-5-i\sqrt{63} }{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B-5-i%5Csqrt%7B63%7D%20%7D%7B-4%7D)
We can break up the fraction to make it easier on our eyes
x = ![\frac{5}{4}\pm\frac{i\sqrt{63} }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D%5Cpm%5Cfrac%7Bi%5Csqrt%7B63%7D%20%7D%7B4%7D)
≈1.9843
x = ![1.25 + 1.9843i\\1.25 - 1.9843i](https://tex.z-dn.net/?f=1.25%20%2B%201.9843i%5C%5C1.25%20-%201.9843i)