By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.
<h3>What is quadratic equation ?</h3>
Any equation of the form
where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .
Given work of Penelope is
![$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+1=4\left(x^{2}+2 x+1\right) \\&0=4(x+2)^{2} \\&0=(x+2)^{2} \\&0=x+2 \\&-2=x\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%26f%28x%29%3D4%20x%5E%7B2%7D%2B8%20x%2B1%20%5C%5C%26-1%3D4%20x%5E%7B2%7D%2B8%20x%20%5C%5C%26-1%3D4%5Cleft%28x%5E%7B2%7D%2B2%20x%5Cright%29%20%5C%5C%26-1%2B1%3D4%5Cleft%28x%5E%7B2%7D%2B2%20x%2B1%5Cright%29%20%5C%5C%260%3D4%28x%2B2%29%5E%7B2%7D%20%5C%5C%260%3D%28x%2B2%29%5E%7B2%7D%20%5C%5C%260%3Dx%2B2%20%5C%5C%26-2%3Dx%5Cend%7Baligned%7D%24%24)
Now we can see that Penelope determined the solutions of the quadratic function by completing the square. so he must have been done as following
![$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+4=4\left(x^{2}+2 x+1\right) \\&3=4(x+2)^{2} \\&\frac{3}{4} =x+2)^{2} \\&\frac{\pm\sqrt3}{2} =x+2 \\&\frac{-2\pm\sqrt3}{2} =x\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%26f%28x%29%3D4%20x%5E%7B2%7D%2B8%20x%2B1%20%5C%5C%26-1%3D4%20x%5E%7B2%7D%2B8%20x%20%5C%5C%26-1%3D4%5Cleft%28x%5E%7B2%7D%2B2%20x%5Cright%29%20%5C%5C%26-1%2B4%3D4%5Cleft%28x%5E%7B2%7D%2B2%20x%2B1%5Cright%29%20%5C%5C%263%3D4%28x%2B2%29%5E%7B2%7D%20%5C%5C%26%5Cfrac%7B3%7D%7B4%7D%20%3Dx%2B2%29%5E%7B2%7D%20%5C%5C%26%5Cfrac%7B%5Cpm%5Csqrt3%7D%7B2%7D%20%3Dx%2B2%20%5C%5C%26%5Cfrac%7B-2%5Cpm%5Csqrt3%7D%7B2%7D%20%3Dx%5Cend%7Baligned%7D%24%24)
By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.
To learn more about quadratic equations visit : brainly.com/question/1214333
0=x^2 -4x+3
0=(x+1) (x+3)
X+1=0 x=-1
X+3=0 x=-3
Answer:
-1/18
Step-by-step explanation:
Let's multiply left and right by 3n:
2 = -12 * 3n =>
-36n = 2
now divide by -36:
n = 2/-36 = -1/18