Question

6x²+ 11x+3=0
m²-18m+81=0
5x²-4x-10=0
3y²+7y-20=0
16x²-24x-1=0

Solve by completing square

Answer 1

Answer:

Step-by-step explanation:

5)General form - ax^2+bx+c=0

D=b^2-4ac

Solution is x=\frac{-b\pm\sqrt{D}}{2a}

Equation is 16x^2 -24x - 1= 0

where, a=16 , b=-24, c=-71

D=b^2-4ac

D=(-24)^2-4(16)(-1)

D=576+64

D=640

Solution is x=\frac{-b\pm\sqrt{D}}{2a}

x=\frac{-(-24)\pm\sqrt{640}}{2(16)}

x=\frac{24\pm8\sqrt{10}}{16}

x=\frac{3\pm\sqrt{10}}{4}

Therefore, The roots are x=\frac{3+\sqrt{10}}{4},\frac{3-\sqrt{10}}{4}

3)formula is

-b+root of(b^2-4ac)/2a      ,    -b-root of(b^2-4ac)/2a

5x^2-4x-10

a=5

b=-4

c=-10

using formula

4+root of (16-4*5*-10)/10      ,   4-root of (16-4*5*-10)/10

4+root of (216)/10                  ,  4-root of (216)/10

4+6 root 6/10                        ,  4-6 root 6/10

2+3 root 6/5                           ,2-3 root 6/5

1)6x^2+11x+3=0

6x^2+9x+2x+3=0

3x(2x+3)+1(2x+3)=0

x=-1/3,-3/2

2)m²-18m+81=0

m^2-9m-9m+81=0

m(m-9)-9(m-9)

m=9,9=9