X²-2x-3 = 0 let's start by grouping the "x"s
(x² - 2x + [?])² - 3 = 0
so, we have a missing fellow there, in order to make the group, a perfect square trinomial, namely to "complete the square", hmmm so the tell-tale fellow is the middle term.
from a perfect square trinomial we know that the middle term is a product of 2 and the "term on the left" and the "term on the right", like
![\bf \begin{array}{cccccllllll} a^2& + &2 a b&+& b^2\\ \downarrow && &&\downarrow \\ a&& && b\\ &\to &( a + b)^2&\leftarrow \end{array}\qquad \qquad \quad \begin{array}{cccccllllll} a^2& - &2 a b&+& b^2\\ \downarrow && &&\downarrow \\ a&& && b\\ &\to &( a - b)^2&\leftarrow \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bcccccllllll%7D%0A%20a%5E2%26%20%2B%20%262%20a%20b%26%2B%26%20b%5E2%5C%5C%0A%5Cdownarrow%20%26%26%20%26%26%5Cdownarrow%20%5C%5C%0A%20a%26%26%20%26%26%20b%5C%5C%0A%26%5Cto%20%26%28%20a%20%2B%20%20b%29%5E2%26%5Cleftarrow%20%0A%5Cend%7Barray%7D%5Cqquad%20%5Cqquad%20%5Cquad%20%0A%5Cbegin%7Barray%7D%7Bcccccllllll%7D%0A%20a%5E2%26%20-%20%262%20a%20b%26%2B%26%20b%5E2%5C%5C%0A%5Cdownarrow%20%26%26%20%26%26%5Cdownarrow%20%5C%5C%0A%20a%26%26%20%26%26%20b%5C%5C%0A%26%5Cto%20%26%28%20a%20-%20%20b%29%5E2%26%5Cleftarrow%20%0A%5Cend%7Barray%7D)
![\bf \textit{therefore}\qquad 2(x)(\boxed{?})=\stackrel{middle~term}{2x}\implies \boxed{?}=\cfrac{2x}{2x}\implies \boxed{?}=1](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Btherefore%7D%5Cqquad%202%28x%29%28%5Cboxed%7B%3F%7D%29%3D%5Cstackrel%7Bmiddle~term%7D%7B2x%7D%5Cimplies%20%5Cboxed%7B%3F%7D%3D%5Ccfrac%7B2x%7D%7B2x%7D%5Cimplies%20%5Cboxed%7B%3F%7D%3D1)
aha!! so our missing fellow is 1.
now, let's keep in mind that all we're doing is borrowing from our very good friend Mr Zero, 0. So if we add 1², we also have to subtract 1².
(x² - 2x + 1² - 1²) - 3 = 0
(x² - 2x + 1) -1 -3 =0
(x - 1)² - 4 = 0
(x - 1)² = 4
Answer:
a. x = 5, m∠FGH = 22°
b. m∠HGI = 22°
c. m∠FGI = 44°
Step-by-step explanation:
Since GH bisects FGI this means it divides the angle in two equal parts.
a. solving for x means equating them:
5x-3 = 6x-8 =>
5x - 6x = 3 - 8 =>
x = 5.
Both m∠FGH and m∠HGI are 5*5-3 = 22°
c. Add both angles: m∠FGH + m∠HGI = 44°
The answer is option 'D' - 211276
Answer:
1. 891
2. 242
Step-by-step explanation:
These are the answers to the question.
The value of the given equation is 0.725
<u>Explanation:</u>
Given:
Equation = ![(0.725)^2 - (0.525 X 0.725) + (0.725 X 0.8)](https://tex.z-dn.net/?f=%280.725%29%5E2%20-%20%280.525%20X%200.725%29%20%2B%20%280.725%20X%200.8%29)
Solving the equation further we get:
![= (0.525625) - (0.380625) + (0.58)\\\\= 0.145 + 0.58\\\\= 0.725](https://tex.z-dn.net/?f=%3D%20%280.525625%29%20-%20%280.380625%29%20%2B%20%280.58%29%5C%5C%5C%5C%3D%200.145%20%2B%200.58%5C%5C%5C%5C%3D%200.725)
Therefore, the value of the given equation is 0.725