Answer:
x = 4 ± ![\sqrt{19}](https://tex.z-dn.net/?f=%5Csqrt%7B19%7D)
Step-by-step explanation:
Given
x² - 8x = 3
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 3 + 16
(x - 4)² = 19 ( take the square root of both sides )
x - 4 = ±
( add 4 to both sides )
x = 4 ±
This can be solved using the
angle bisector theorem. Note that line segment AD is the angle bisector of triangle DAB from angle DAB. Therefore, we know that the ratios
![\frac{\text{AD}}{\text{CD}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BAD%7D%7D%7B%5Ctext%7BCD%7D%7D)
and
![\frac{\text{AB}}{\text{CB}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BAB%7D%7D%7B%5Ctext%7BCB%7D%7D)
are equal. Solving, we get
![\frac{\text{12.2}}{\text{7.8}}=\frac{\text{AB}}{\text{6.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7B12.2%7D%7D%7B%5Ctext%7B7.8%7D%7D%3D%5Cfrac%7B%5Ctext%7BAB%7D%7D%7B%5Ctext%7B6.5%7D%7D)
. Cross multiplying, we get
![79.3 = 7.8x](https://tex.z-dn.net/?f=79.3%20%3D%207.8x)
, and solving this equation we get
![x = 10.1666... \approx 10.2](https://tex.z-dn.net/?f=x%20%3D%2010.1666...%20%5Capprox%2010.2)
.
10.2 is your answer.
Answer:
![\Large{\bold{\frac{4x\:+\:1}{x\:+\:6}}}](https://tex.z-dn.net/?f=%5CLarge%7B%5Cbold%7B%5Cfrac%7B4x%5C%3A%2B%5C%3A1%7D%7Bx%5C%3A%2B%5C%3A6%7D%7D%7D)
Step-by-step explanation:
![(8x\:-\:4x\:+\:1) ÷ (x\:+\:6)](https://tex.z-dn.net/?f=%288x%5C%3A-%5C%3A4x%5C%3A%2B%5C%3A1%29%20%C3%B7%20%28x%5C%3A%2B%5C%3A6%29)
![\frac{8x\:-\:4x\:+\:1}{x\:+\:6}](https://tex.z-dn.net/?f=%5Cfrac%7B8x%5C%3A-%5C%3A4x%5C%3A%2B%5C%3A1%7D%7Bx%5C%3A%2B%5C%3A6%7D)
![\frac{4x\:+\:1}{x\:+\:6}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%5C%3A%2B%5C%3A1%7D%7Bx%5C%3A%2B%5C%3A6%7D)
Answer:
![\boxed{ \bold{ \huge{ \boxed{ \sf{3 {i}^{2} + 6i}}}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Chuge%7B%20%5Cboxed%7B%20%5Csf%7B3%20%7Bi%7D%5E%7B2%7D%20%20%2B%206i%7D%7D%7D%7D%7D)
Step-by-step explanation:
![\sf{(2 + i)(i + 2i)}](https://tex.z-dn.net/?f=%20%5Csf%7B%282%20%2B%20i%29%28i%20%2B%202i%29%7D)
Use the distribute property to multiply each term of the first binomial by each term of the second binomial.
⇒![\sf{2(i + 2i) + i(i + 2i)}](https://tex.z-dn.net/?f=%20%5Csf%7B2%28i%20%2B%202i%29%20%2B%20i%28i%20%2B%202i%29%7D)
⇒![\sf{2i + 4i + {i}^{2} + 2 {i}^{2} }](https://tex.z-dn.net/?f=%20%5Csf%7B2i%20%2B%204i%20%2B%20%20%7Bi%7D%5E%7B2%7D%20%20%2B%202%20%7Bi%7D%5E%7B2%7D%20%7D)
Collect like terms
⇒![\sf{3 {i}^{2} + 6i}](https://tex.z-dn.net/?f=%20%5Csf%7B3%20%7Bi%7D%5E%7B2%7D%20%20%2B%206i%7D)
Hope I helped!
Best regards!
Answer:
none...
Step-by-step explanation: