anonymous
  • anonymous
How do you complete the square to form perfect trinomial for 4x^2=14x+8
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
x=4, -1/2
anonymous
  • anonymous
How did you do it tho steps pleases
anonymous
  • 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
  • anonymous
fan and medal please
anonymous
  • anonymous
how do I do that
anonymous
  • anonymous
fan me, go to my name and something will come and it says 'become a fan', and click that
anonymous
  • anonymous
Thanks lol can you also help me with others?
anonymous
  • anonymous
sure
anonymous
  • anonymous
4x^2+5X+2=0
anonymous
  • anonymous
Also on the first one how did you get -12,4 but you said it's 4,1/2
mathstudent55
  • mathstudent55
He got -1/2 and 4. He just forgot to write the / between the -1 and the 2.
anonymous
  • anonymous
ohh okay thank you!!
mathstudent55
  • mathstudent55
Do you just need to solve the equation using any method, or do you have to use the complete the square method?
anonymous
  • anonymous
it just says complete the square to form a perfect square trinomial
mathstudent55
  • 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
  • anonymous
thank your a life saver!
mathstudent55
  • 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
  • anonymous
wait so idont have to have the 4,1/2
mathstudent55
  • 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
  • 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
  • mathstudent55
Now we are just completing the square.
mathstudent55
  • mathstudent55
We are ready for the next step. This is the actual step that completes the square.
mathstudent55
  • 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
  • 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
  • mathstudent55
If all you need to do is complete the square, you are done now.
anonymous
  • anonymous
im so confused lol
anonymous
  • anonymous
is that a perfect square trinomial?
mathstudent55
  • mathstudent55
Yes. The left side is a perfect square trinomial when written as \(x^2 - \dfrac{7}{2}x + \dfrac{49}{16} \)
mathstudent55
  • 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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