## anonymous one year ago How do you complete the square to form perfect trinomial for 4x^2=14x+8

1. anonymous

x=4, -1/2

2. anonymous

How did you do it tho steps pleases

3. 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

4. anonymous

5. anonymous

how do I do that

6. anonymous

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

7. anonymous

Thanks lol can you also help me with others?

8. anonymous

sure

9. anonymous

4x^2+5X+2=0

10. anonymous

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

11. mathstudent55

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

12. anonymous

ohh okay thank you!!

13. mathstudent55

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

14. anonymous

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

15. 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.

16. anonymous

17. 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. $$4x^2 - 14x = 8$$

18. anonymous

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

19. 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.

20. 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.

21. mathstudent55

Now we are just completing the square.

22. mathstudent55

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

23. 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.

24. 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.

25. mathstudent55

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

26. anonymous

im so confused lol

27. anonymous

is that a perfect square trinomial?

28. mathstudent55

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

29. 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.