Solve by completing the square?

Question

x^2 + 6x = 7

Please tell how you got the answer too because I need to understand it for a test coming up. Thanks so much.

Answer 1

[04]
x^2+6x=7
x^2+2*x*3+(3)^2=7+9[adding (3)^2 or 9 to both sides]
(x+3)^2=16
(x+3)^2=(4)^2
(x+3)=+-4 [square-rooting both sides]
x= -3+-4
=-7 or 1

Answer 2

x^2 + 6x = 7

Bring the 7 to the left-hand side (L.H.S)

=> x^2 + 6x - 7 = 0

Divide the 6 by 2 and you will get 3 ( 6/2 = 3) After that, squared the 3 which will give you 9

Then, add the 9 into the equation

=> x^2 + 6x + 9 - 7

Wait! After you have added the 9 into the equation, you must remember to subtract the 9 from the equation. But why? Reason is very simple; the objective of completing the square is to keep the polynomial the same, and just change what it looks like a little bit.

=> x^2 + 6x + 9 - 7 - 9

See this
=> x^2 + 6x + 9
This could be written as (x + 3)^2

Now, see this
=> -7 -9
= -16

So, combine all the 'equations' together and you will get:

=> (x + 3)^2 - 16

Finally, to solve it...

=> (x+3)^2 = 16
x+3= +/-4
x=-7 or x = 1

Answer 3

The sqrt of 9 is 3 so, if you add 9 to both sides of the equation it becomes: x^2+6x+9=16 Factoring you have (x+3)^2=16 Take the sqrt of both sides and you get x+3=4. Since a sqrt can also be negative 4 could also be -4. This would make x = -7 or 1.

Answer 4

So the first thing you have to do is factor:

you move 7 to the left and

Set this equal to zero: so the equation becomes
x^2+6x-7=0

Factor this such that the sum of the factors equate to 6(The middle part of the equation)
(X-1) and (X+7) satisfies the factoring
solving these by equating to zero
(X-1)=0 or (X+7)=0

you get the value for X=1 or
-7(Negative 7).

X = 1,-7 are the values.

Answer 5

Step 1: Write out the equation
x^2 + 6x = 7

Step 2: Get all of the numbers on one side (in this case, subtract 7 from both sides)
x^2 + 6x - 7 = 0

Step 3: Factor the equation so that when you F.O.I.L. the equation you get the equation in step 2.... to do this you you want the two numbers to multiply to get -7 and add to get 6
(x-7)(x+1)=0

Step 4: Set each equation to 0
x-7=0 x-1=0

Step 5: Solve each equation
x=7 x=1

Answer 6

x^2 + 6x = 7
x^2 + 6x +9 = 16 (add 9 to each side to make left side a perfect square trinomial)
(x+3)^2 = 16 (factor the left side)
x+3 =+-4 (take the root of each side)
x = 1 or -7 (subtract 3 from 4 adn -4)

Answer 7

ax^2 + bx - c = 0
a*(-c) = g
b = h
think the number that fit to solve the x

x^2 + 6x - 7 = 0
g = -7
h = 6
think what number that the sum is 6 and the multiplication is -7
first just look at the number -7-> what are the factors of -7?
-> -1 * 7 or 1*-7
but we know that the sum must be 6
so figuring this out: the only probability is -1 and 7

process:
x^2 + 6x - 7 = 0
(x-1) (x+7) = 0 ---- we got above
then x1= 1; x2 = -7

Answer 8

first make put it as a quadratic (equal to zero):

x^2 +6x - 7 = 0

Then set it up like so:

x^2 + 6x + ___= 7 + ___
(notice the 7 on the other side with opposite sign-- no longer negative)

Then ALWAYS divide 2 by the number 6x (or whatever number is there)
**in this case = a positive 3
----> Then square whatever number you get and fill in the number 9 at the blanks:

x^2 + 6x + _9_= 7 + _9_

then add the 7 and 9 (because you can--there are no X's)
so now you have

x^2 + 6x + __9__ = 16

now ignore the rest of the problem--but remember you have a POSTIVE three in that last blank (so whatever number you have in your last blank is the number you use)
you then set it up :

(x+3)^2 = 16 **( its an x PLUS three because we got a positive three when we divided 6x by 2)

Now you have to get rid of the squared on the part (x+3)^2
so we square root both sides

now the problem reads

x+3 = Square Root 16
but we need to solve for x still
and fix the sqaure root 16 to equal plus or minus 4
so subtract the three to the other side

finally:

X = 3 +/- 4
x=-7 x=1

Answer 9

x^2 + 6x = 7

first of all you bring it one side

x^2+6x-7=0

then seperate out the quadratic, leaving the -7 out. Then you will take half of the number in front of the seond x (6)and square it

6/2=3
3^2=9

then put it at the end of the quadratic, also putting the negative of 9 on the outside

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

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

then factor the quadratic

(x+3)^2-16=0

and square both sides


(x+3)^2 = 16
x+3= +/-4
x=-7,1

just IM or email if you need anymore help

Answer 10

x² + 6x + 9 = 7 + 9
(x + 3)² = 16
x + 3 = ± 4
x = - 3 ± 4
x = 1 , x = - 7

Answer 11

x^2 + 6x = 7
x^2 + 6x + (6/2)^2 = 7 + (6/2)^2
(x + 3)^2 = 16
(x + 3) = +4, (x + 3) = -4
x = 1, x = -7