Find the measure of angle dbc if the measure of angle abc =5x+3 and angle abd is congruent to angle dbc

and Step-by-step explanation:

y=6x² +2x - 20

let a=6  

let b= 2

let c = -20

Using Quadratic Formula by hand Using Factoring and the Zero Property Product Using Completing the Square Using Graphing on the Calculator

using Quadratic Formula

-b ± √( b² - 4ac)

             2a

-2 ± √( 2² - 4*6(-20))

             2*6

-2 ± √( 2² - 4*6(-20))

              2*6

-2 ± √(484)

       2*6

20/12 = 5/3      

-24/12 = -2

the answers are 5/3 ;  -2

use by Factoring

0=6x² +2x - 20

0 =2( 3x² +x - 10)

   =2 ( 3x-5) ( x+2)

by using the zero product property

3x-5 = 0

x+2 = 0

3x=5        

x =-2

x = 5/3    

x = -2

by using completing the square

y=6x² +2x - 20   Add 20

20=6x² +2x        Divide by 6

20/6 = x² +2/6x

10/3 = x^2 +1/3x    Take the coefficient of x and divide by 2

1/3 /2 = 1/6             Square it

(1/6) ² = 1/36        Add it to both side s

10/3 + 1/36 = x² +1/3x+ 1/36

120/36 + 1/36  = ( x+ 1/6)²

121/ 36= ( x+ 1/6)²  Take the square root of both side

√(121/ 36) = √( ( x+ 1/6)²)

±11/6 = x+1/6          Subtract 1/6 from both side

-1/6 ±11/6 = x

-1/6 - 11/6 = x      

-1/6 + 11/6 = x

-12/6 =x                

10/6 =x

x = -2  

x = 5/3

by using a graphing computer