Question

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

Answer 1

x=4, -1/2

Answer 2

How did you do it tho steps pleases

Answer 3

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

Answer 4

fan and medal please

Answer 5

how do I do that

Answer 6

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

Answer 7

Thanks lol can you also help me with others?

Answer 8

sure

Answer 9

4x^2+5X+2=0

Answer 10

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

Answer 11

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

Answer 12

ohh okay thank you!!

Answer 13

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

Answer 14

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

Answer 15

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.

Answer 16

thank your a life saver!

Answer 17

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.

\(4x^2 - 14x = 8\)

Answer 18

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

Answer 19

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.

Answer 20

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.

Answer 21

Now we are just completing the square.

Answer 22

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

Answer 23

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.

Answer 24

\(\left(x - \dfrac{7}{4} \right)^2 = \dfrac{32}{16} + \dfrac{49}{16} \)

\(\left(x - \dfrac{7}{4} \right)^2 = \dfrac{81}{16} \)

Ok, the complete the square step is finished.

Answer 25

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

Answer 26

im so confused lol

Answer 27

is that a perfect square trinomial?

Answer 28

Yes. The left side is a perfect square trinomial when written as

\(x^2 - \dfrac{7}{2}x + \dfrac{49}{16} \)

Answer 29

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.