Question

Please show all steps and explain what you did thoroughly, thank you for your time and help.

Answer 1

Answer:

Step-by-step explanation:

1) x² + 6x + 11 = 0

a = coefficient of x² = 1

b = coefficient of x = 6

c = Constant = 11

Roots = (-b ± √b² - 4ac)/2a

$D = \sqrt{b^{2}-4ac}\\\\=\sqrt{6^{2}-4*1*11}\\\\=\sqrt{36-44}\\\\=\sqrt{-8}\\\\=\sqrt{8i^{2}}\\\\ = 2i\sqrt{2}$

Roots = $\dfrac{-6 \± 2i\sqrt{2}}{2}$

          $= \dfrac{2(-3 \± i\sqrt{2})}{2}\\\\=-3 \± i\sqrt{2}$

2) 2x² - 16x = 50

Divide the whole equation by 2

x² - 8x = 25

Divide the coefficient of x  (i. e 8 ) by 2 = 8/2 = 4, Now add 4 to both sides of the equation

x² - 8x + 4 = 25 + 4

x² - 2*4*x + 2² = 29

(x - 2)² = 29

Take square root both side

$x - 2 = \± \sqrt{29}\\\\x = 2 \± \sqrt{29}$