eddy2017
Elite Member
- Joined
- Oct 27, 2017
- Messages
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Dear tutors, following Otis' advice I am opening a new thread so you can check if I did everything well when I tried to complete the sqaure in this equation.
Complete the square in the given equation:
X^2 + 12x + 32=0
Step 1
TAKE EVERYTHING THAT HAS AN X TERM IN IT AND PUT IT ON ONE SIDE OF THE EQUAL SIGN ( the rest goes on the other side of the equal sign)
So, this means that 32 needs to go to the other side, and we do that subtracting 32 from both sides
x^2 + 12x + 32-32 =0-32
x^2 + 12x =-32
step 2
let’s put the left hand side into this form:
x^2 + 12x + ___ (some number)= -32
we don’t know what the number is, but our goal is try to make this into a perfect square.
Step 3
Now let’s determine what that unknown value is (let’s call it c value)
Whatever it is we need to find a number that when we add it to itself we get 12 and when we multiply it by itself we get the missing number for the blank space, so,
We need to complete the square and here’s a way to that,
Take the b value in our expression= 12 and divide it by 2 = 6
Now, let's take 6 and square it =6^2= 36
Then, 36 is our c value, the value that goes in the blank,
x^2 + 12x + ___=-32
x^2 + 12x + 36= so this is what we call a perfect square,
but since we added 36 to the left hand side we need to do the same to the right hand side.
x^2 + 12x + 36 =-32+36 (this will reduce to 4 on the right hand side)
x^2 + 12x + 36 =4
step 4
now that we have this trinomial on the left, let’s factor it.
let's keep in mind that this should be a perfect square.
x^2 + 12x + 36 =4
when we factor it, we get,
(x+6)(x+6)= 4 6 because it is half the value of term b (or second term).
It is a perfect square because we have two identical binomials being multiplied together,
And notice the value of 6, what happens when we add it to itself? We get 12
And when we multiply it together we get 36.
So, (x+6)+(x+6)=4
(x+6)^2 = 4
And now that we have it on this form we are ready to solve for x
To solve this equation for x, we need to remove the square.
Step 6
We need to take the square of both sides, so,
√(x+6)^2= √4
x+6= ±2
now, we have a positive and a negative value for 2.
Step 7
Let’s split these two values into two different problems and solve them.
X+6 =+2 and x+6= -2
Let’s solve for x in both problems and we get two different answers
X=-4 and x=-8
And now we have our answers. X is -4 and x is -8
If you take either one of these values and plug them into the original equation the left hand side should equal 0.
Let’s check our answer.
Let’s plug -4 and see if we get 0
X^2 + 12x + 32=0
(-4)^2 + 12(-4)+32= 0
This reduces to,
16-48+32=0
The left hand side reduces to 0 and we are left with
0=0 we get a value that equals 0 so that means that -4 is one of our answers
Now let’s do the same thing with our other value, -8
X^2 + 12x + 32=0
(-8)^2+12(-8)+32=0
Simplifyin’ we have
64-96+32=0
Left side reduces to 0
Making our value of -8 a true one.
thanks in advance
Complete the square in the given equation:
X^2 + 12x + 32=0
Step 1
TAKE EVERYTHING THAT HAS AN X TERM IN IT AND PUT IT ON ONE SIDE OF THE EQUAL SIGN ( the rest goes on the other side of the equal sign)
So, this means that 32 needs to go to the other side, and we do that subtracting 32 from both sides
x^2 + 12x + 32-32 =0-32
x^2 + 12x =-32
step 2
let’s put the left hand side into this form:
x^2 + 12x + ___ (some number)= -32
we don’t know what the number is, but our goal is try to make this into a perfect square.
Step 3
Now let’s determine what that unknown value is (let’s call it c value)
Whatever it is we need to find a number that when we add it to itself we get 12 and when we multiply it by itself we get the missing number for the blank space, so,
We need to complete the square and here’s a way to that,
Take the b value in our expression= 12 and divide it by 2 = 6
Now, let's take 6 and square it =6^2= 36
Then, 36 is our c value, the value that goes in the blank,
x^2 + 12x + ___=-32
x^2 + 12x + 36= so this is what we call a perfect square,
but since we added 36 to the left hand side we need to do the same to the right hand side.
x^2 + 12x + 36 =-32+36 (this will reduce to 4 on the right hand side)
x^2 + 12x + 36 =4
step 4
now that we have this trinomial on the left, let’s factor it.
let's keep in mind that this should be a perfect square.
x^2 + 12x + 36 =4
when we factor it, we get,
(x+6)(x+6)= 4 6 because it is half the value of term b (or second term).
It is a perfect square because we have two identical binomials being multiplied together,
And notice the value of 6, what happens when we add it to itself? We get 12
And when we multiply it together we get 36.
So, (x+6)+(x+6)=4
(x+6)^2 = 4
And now that we have it on this form we are ready to solve for x
To solve this equation for x, we need to remove the square.
Step 6
We need to take the square of both sides, so,
√(x+6)^2= √4
x+6= ±2
now, we have a positive and a negative value for 2.
Step 7
Let’s split these two values into two different problems and solve them.
X+6 =+2 and x+6= -2
Let’s solve for x in both problems and we get two different answers
X=-4 and x=-8
And now we have our answers. X is -4 and x is -8
If you take either one of these values and plug them into the original equation the left hand side should equal 0.
Let’s check our answer.
Let’s plug -4 and see if we get 0
X^2 + 12x + 32=0
(-4)^2 + 12(-4)+32= 0
This reduces to,
16-48+32=0
The left hand side reduces to 0 and we are left with
0=0 we get a value that equals 0 so that means that -4 is one of our answers
Now let’s do the same thing with our other value, -8
X^2 + 12x + 32=0
(-8)^2+12(-8)+32=0
Simplifyin’ we have
64-96+32=0
Left side reduces to 0
Making our value of -8 a true one.
thanks in advance
