Quadratic equations and finding the square help?

Question

Completing the square. 
1.) X²-10x+6=0 

Solve the quadratic formula 
2.) 24= 8(y-2)² 
3.) 5x²=4x+2 
4.) 16= 8x-x² 
5.) 5x²+13x-3=-6 
6.) 3x²+2x=6 

Please explain to me how you would get the answer. Thanks.

 

 

Answer 1

1) x^2-10x+6 = 0

Add 19 to each side, for completing square.

x^2-10x+6+19 = 0+19

x^2-10x+25 = 19

(x-5)^2 = 19

Apply squre root each side.

√19 = √(x-5)^2

±√19 = √(x-5)^2

Add 5 to each side.

5±√19 = x-5+5

x = 5±√19

Solution x = 5+√19 or x = 5-√19

2.) 24 = 8(y-2)²

Divide by 8 to each side.

24/8 = 8(y-2)^2/8

3 = (y-2)^2

Apply squre root to each side..

√3 = √(y-2)^2

±√3 = y-2

Add 2 to each side.

±√3+2 = y-2+2

±√3+2 = y

Solution y = 2+√3 , y = 2-√3

4) 16= 8x-x²

Bring the all terms to one side.

16-8x+x^2 = 0

x^2-8x+16 = 0

x^2-4x-4x +16 = 0

x(x-4)-4(x-4) = 0

(x-4)(x-4) =0

Solution x = 4

3.) 5x²=4x+2
Bring all terms to one side.

5x^2-4x-2 = 0

x = [-(-4)±.√(-4)^2-4*5*-2]/2*5

x = 4±.√(16+40)/10

x = 4±.√(56)/10

x = 4±.√(4*14)/10

x = 4±.2√(14)/10

Take common out 2.

x = 2(2±.√14)/10

x = (2±.√14)/5

x = (2±√14)/5

Solution x = (2+√14)/5 or x = (2-√14)/5

5.) 5x²+13x-3=-6

Add 6 to each side.

5x^2+13x-3+6 = -6+6

5x^2+13x+3 = 0

x = [-13±√(169-4*5*3)/2*5

x = [-13±√(169-60)]/10

x = (-13±√109)/10

Solution x = (-13+√109)/10 or x = (-13-√109)/10

Answer 2

6.) 3x²+2x=6

Subtract 6 from each side.

3x^2+2x-6 = +6-6

3x^2+2x-6 = 0

x = [-2±√(4-4*3*-6)]/(2*-6)

x = [-2±√(4+48)]/-12

x = (-2±√52)/-12

x = (-2±√13*4)/-12

x = (-2±2√13)/-12

Take common out 2

x = 2(-1±√13)/-12

x = (-1±√13)/-6

x = (-1+√13)/-6     or    x =(-1-√13)/-6

Solution x = (1-√13)/6         or   x = (1+√13)/6

Comments

Solution of 3x²+2x = 6 is

 

Answer 3

6) The equation 3x² + 2x = 6

Compare it to quadratic equation 

Roots are

Solution