2.4k views
0 votes
COMPLETING THE SQUARE

COMPLETING THE SQUARE-example-1
User Sachy
by
7.1k points

1 Answer

4 votes

Answer:

13.
x=1,-7

14.
x=-3+√(14) and
x=-3-√(14)

Explanation:

to solve the quadratic equation(
ax^(2) +bx+c=0) using completing the squares method:

Step1: divide the equation by a to make it in the form
x^(2) +(b)/(a)x+(c)/(a) =0

Step2: add
((b)/(2a))^(2) on both sides of the equation to get the eqaution:


x^(2) +(b)/(a)x+((b)/(2a))^(2) +(c)/(a)=((b)/(2a))^(2)

Step3: rearrange them to get the square.


(x+(b)/(2a) )^(2)=((b)/(2a))^(2)-(c)/(a)


x= -(b)/(2a)+\sqrt{((b)/(2a))^(2)-(c)/(a)} and


x= (b)/(2a)+\sqrt{((b)/(2a))^(2)-(c)/(a)}

Now getting on to the question:

13.
x^(2) +6x=7

a=1; b=6; c=-7

adding
(b)/(2a)^(2) = (6)/(2*1)^(2) =3^(2) =9 on both sides


x^(2) +6x+9=7+9


x^(2) +6x+9=16


(x+3)^(2)=16


x+3=√(16)


x+3=4 and
x+3=-4


x=1,-7

14.
x^(2) +6x=5

a=1; b=6; c=-5

adding
(b)/(2a)^(2) = (6)/(2*1)^(2) =3^(2) =9on both sides


x^(2) +6x+9=5+9


x^(2) +6x+9=14


(x+3)^(2)=14


x+3=√(14)


x+3=√(14) and
x+3=-√(14)


x=-3+√(14) and
x=-3-√(14)

User Almendar
by
7.0k points