Solve the quadratic equation given below.

(12x – 27)^2 = 256

x

2

+

12

x

−

64

=

0

⟹

x

2

+

12

x

=

64.

x

2

+

12

x

=

64

⟹

(

4

∗

1

)

(

x

2

+

12

x

)

=

(

4

∗

1

)

64

⟹

4

x

2

+

48

x

=

256

All this is straight forward. This method now requires you to add the square of the original coefficient of x to both sides of the equation.

The original coefficient is 12 so its square is 144.

4

x

2

+

48

x

=

256

⟹

4

x

2

+

48

x

+

144

=

256

+

144

=

400

⟹

4

(

x

2

+

12

x

+

36

)

=

20

2

⟹

2

2

(

x

+

6

)

2

=

20

2

.

Step-by-step explanation:

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2