Answer:
![\dfrac{9}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7B2%7D)
Step-by-step explanation:
You can do this using the quadratic equation:
![x =\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D)
Let's first setup our expression:
4x² + 12x = 135
the quadratic formula is:
ax² + bx + c = 0
4x² + 12x - 135 = 0
Then:
a = 4
b = 12
c = -135
Now we plug in our coefficients and solve:
![x =\dfrac{-12\pm\sqrt{12^{2}-4(4)(-135)}}{2(4)}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-12%5Cpm%5Csqrt%7B12%5E%7B2%7D-4%284%29%28-135%29%7D%7D%7B2%284%29%7D)
We solve for both to determine the positive one:
![x =\dfrac{-12- \sqrt{12^{2}-4(4)(-135)}}{2(4)}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-12-%20%5Csqrt%7B12%5E%7B2%7D-4%284%29%28-135%29%7D%7D%7B2%284%29%7D)
![x =\dfrac{-12- \sqrt{144+2160}}{8}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-12-%20%5Csqrt%7B144%2B2160%7D%7D%7B8%7D)
![x =\dfrac{-12- \sqrt{2304}}{8}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-12-%20%5Csqrt%7B2304%7D%7D%7B8%7D)
![x =\dfrac{-12- 48}{8}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-12-%2048%7D%7B8%7D)
![x =\dfrac{-60}{8} = \dfrac{-15}{2}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B-60%7D%7B8%7D%20%3D%20%5Cdfrac%7B-15%7D%7B2%7D)
So if you are looking for a positive solution, just take the positive one as x.
Answer:
343
Step-by-step explanation:
7 cubed = 7 x 7 x 7 = 343
so, 343 is a perfect cube.
Working is a bit of a mess, but vertically she's correct, but she's incorrect horizontally