How do you complete the square to form perfect trinomial for 4x^2=14x+8

- anonymous

How do you complete the square to form perfect trinomial for 4x^2=14x+8

- jamiebookeater

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- anonymous

x=4, -1/2

- anonymous

How did you do it tho steps pleases

- anonymous

1 Move all terms to one side
4x2−14x−8=0
2 Factor out the common term 2
2(2x2−7x−4)=0
3 Factor 2x2−7x−4
1. Multiply 2 by -4, which is -8.
2. Ask: Which two numbers add up to -7 and multiply to -8?
3. Answer: 1 and -8
4. Rewrite −7x as the sum of x and −8x:
2(2x2+x−8x−4)=0
4 Factor out common terms in the first two terms, then in the last two terms
2(x(2x+1)−4(2x+1))=0
5 Factor out the common term 2x+1
2(2x+1)(x−4)=0
6 Solve for x
1. Ask: When will (2x+1)(x−4) equal zero?
2. Answer: When 2x+1=0 or x−4=0.
3. Solve each of the 2 equations above:
x=−12,4

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- anonymous

fan and medal please

- anonymous

how do I do that

- anonymous

fan me, go to my name and something will come and it says 'become a fan', and click that

- anonymous

Thanks lol can you also help me with others?

- anonymous

sure

- anonymous

4x^2+5X+2=0

- anonymous

Also on the first one how did you get -12,4 but you said it's 4,1/2

- mathstudent55

He got -1/2 and 4. He just forgot to write the / between the -1 and the 2.

- anonymous

ohh okay thank you!!

- mathstudent55

Do you just need to solve the equation using any method, or do you have to use the complete the square method?

- anonymous

it just says complete the square to form a perfect square trinomial

- mathstudent55

Then you need to complete the square.
This is how you complete the square to solve a quadratic equation.
I'll show you the steps.

- anonymous

thank your a life saver!

- mathstudent55

Your equation is:
\(4x^2=14x+8\)
1. You need the x^2 term and the x term to the left side, and the number on the right side. All we need to do is subtract 14x from both sides.
\(4x^2 - 14x = 8\)

- anonymous

wait so idont have to have the 4,1/2

- mathstudent55

2. The first term must be just x^2 (without a coefficient). If it is not, then divide both sides of the equation by the coefficient of the x^2 term. In our case, we divide the equation by 4 on both sides to get:
\(\dfrac{4}{4}x^2 - \dfrac{14}{4}x = \dfrac{8}{4} \)
which simplifies to
\(x^2 - \dfrac{7}{2}x = 2 \)
As you can see, we now have just x^2 for the x^2 term.

- mathstudent55

4 and -1/2 are the solutions of the equation. If we complete the square and continue, we will get to 4 and -1/2. You'll see.

- mathstudent55

Now we are just completing the square.

- mathstudent55

We are ready for the next step. This is the actual step that completes the square.

- mathstudent55

3. Take half of the coefficient of the x-term, and square it. Add it to both sides.
\(x^2 - \dfrac{7}{2}x = 2 \)
Half of 7/4 is 7/4. The square of 7/4 is 49/16. We add 49/16 to both sides.
\(x^2 - \dfrac{7}{2}x + \dfrac{49}{16} = 2 + \dfrac{49}{16} \)
Now we write the left side as the square of a binomial, and we add the fractions on the right side.

- mathstudent55

\(\left(x - \dfrac{7}{4} \right)^2 = \dfrac{32}{16} + \dfrac{49}{16} \)
\(\left(x - \dfrac{7}{4} \right)^2 = \dfrac{81}{16} \)
Ok, the complete the square step is finished.

- mathstudent55

If all you need to do is complete the square, you are done now.

- anonymous

im so confused lol

- anonymous

is that a perfect square trinomial?

- mathstudent55

Yes. The left side is a perfect square trinomial when written as
\(x^2 - \dfrac{7}{2}x + \dfrac{49}{16} \)

- mathstudent55

Once you complete the square, you can solve the quadratic equation.
Take square roots of both sides:
\(\sqrt{\left(x - \dfrac{7}{4} \right)^2} = \pm \sqrt{\dfrac{81}{16}} \)
\(x - \dfrac{7}{4} = \pm\dfrac{9}{4} \)
Now separate the equation into two equations:
\(x - \dfrac{7}{4} = \dfrac{9}{4} \) or \(x - \dfrac{7}{4} = -\dfrac{9}{4} \)
\(x = \dfrac{9}{4} + \dfrac{7}{4} \) or \(x = - \dfrac{9}{4} +\dfrac{7}{4} \)
\(x = \dfrac{16}{4} \) or \(x = - \dfrac{2}{4}\)
\(x = 4\) or \(x = -\dfrac{1}{2} \)
As you can see, we get x = 4 or x = -1/2, as you had gotten before.

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