For the given equation;
We shall begin by expanding the parenthesis on the left side, after which we would combine all terms on and move all of them to the left side, which shall yield a quadratic equation. Then we shall solve.
Let us begin by expanding the parenthesis;
Now that we have expanded the left side of the equation, we would have;
We shall now solve the resulting quadratic equation using the quadratic formula as follows;
![\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=9,b=-30,c=150 \\ x=\frac{-(-30)\pm\sqrt[]{(-30)^2-4(9)(150)}}{2(9)} \\ x=\frac{30\pm\sqrt[]{900-5400}}{18} \\ x=\frac{30\pm\sqrt[]{-4500}}{18} \\ x=\frac{30\pm\sqrt[]{-900\times5}}{18} \\ x=\frac{30\pm\sqrt[]{-900}\times\sqrt[]{5}}{18} \\ x=\frac{30\pm30i\sqrt[]{5}}{18} \\ \text{Therefore;} \\ x=\frac{30+30i\sqrt[]{5}}{18},x=\frac{30-30i\sqrt[]{5}}{18} \\ \text{Divide all through by 6, and we'll have;} \\ x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20%5Ctext%7BWhere%3B%7D%20%5C%5C%20a%3D9%2Cb%3D-30%2Cc%3D150%20%5C%5C%20x%3D%5Cfrac%7B-%28-30%29%5Cpm%5Csqrt%5B%5D%7B%28-30%29%5E2-4%289%29%28150%29%7D%7D%7B2%289%29%7D%20%5C%5C%20x%3D%5Cfrac%7B30%5Cpm%5Csqrt%5B%5D%7B900-5400%7D%7D%7B18%7D%20%5C%5C%20x%3D%5Cfrac%7B30%5Cpm%5Csqrt%5B%5D%7B-4500%7D%7D%7B18%7D%20%5C%5C%20x%3D%5Cfrac%7B30%5Cpm%5Csqrt%5B%5D%7B-900%5Ctimes5%7D%7D%7B18%7D%20%5C%5C%20x%3D%5Cfrac%7B30%5Cpm%5Csqrt%5B%5D%7B-900%7D%5Ctimes%5Csqrt%5B%5D%7B5%7D%7D%7B18%7D%20%5C%5C%20x%3D%5Cfrac%7B30%5Cpm30i%5Csqrt%5B%5D%7B5%7D%7D%7B18%7D%20%5C%5C%20%5Ctext%7BTherefore%3B%7D%20%5C%5C%20x%3D%5Cfrac%7B30%2B30i%5Csqrt%5B%5D%7B5%7D%7D%7B18%7D%2Cx%3D%5Cfrac%7B30-30i%5Csqrt%5B%5D%7B5%7D%7D%7B18%7D%20%5C%5C%20%5Ctext%7BDivide%20all%20through%20by%206%2C%20and%20we%27ll%20have%3B%7D%20%5C%5C%20x%3D%5Cfrac%7B5%2B5i%5Csqrt%5B%5D%7B5%7D%7D%7B3%7D%2Cx%3D%5Cfrac%7B5-5i%5Csqrt%5B%5D%7B5%7D%7D%7B3%7D%20%5Cend%7Bgathered%7D)
ANSWER:
![x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5%2B5i%5Csqrt%5B%5D%7B5%7D%7D%7B3%7D%2Cx%3D%5Cfrac%7B5-5i%5Csqrt%5B%5D%7B5%7D%7D%7B3%7D)
Answer:
when the rest of the variables are held constant
Step-by-step explanation:
Answer:
Vertical stretch of factor of 3
translated to the right 2
translated up 5
Step-by-step explanation:
Answer:
x = 1/18
Step-by-step explanation:
2/3x = 12
multiply both sides by 3x
2/3x(3x) = 12(3x)
2 = 36x
x = 1/18
Answer:
True
Step-by-step explanation:
This equation correctly represents the total cost of the food that the friends ended up paying for the popcorn and sodas. In this expression, the cost of each individual soda is represented by the variable x which is multiplied by 4 since each one of the four friend's purchased their own soda. After making this multiplication process that product is added to the initial $12 that they all spent together on the popcorn.
