1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
galben [10]
2 years ago
13

Determine the next step for solving the quadratic equation by completing the square.

Mathematics
1 answer:
nexus9112 [7]2 years ago
8 0

\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2

the idea behind the completion of the square is simply using a perfect square trinomial,  hmmm usually we do that by using our very good friend Mr Zero, 0.

if we look at the 2nd step, we have a group as x² - x, hmmm so we need a third element, which will be squared.

keeping in mind that the middle term of the perfect square trinomial is simply the product of the roots of "a" and "b",  so in this case the middle term is "-x", and the 1st term is x², so we can say that

\stackrel{middle~term}{2(\sqrt{x^2})(\sqrt{b^2})~}~ = ~~\stackrel{middle~term}{-x}\implies 2xb~~ = ~~~~ = ~~-x \\\\\\ b=\cfrac{-x}{2x} \implies b=-\cfrac{1}{2}

so that means that our missing third term for a perfect square trinomial is simply 1/2, now we'll go to our good friend Mr Zero, if we add (1/2)², we have to also subtract (1/2)², because all we're really doing is borrowing from Zero, so we'll be including then +(1/2)² and -(1/2)², keeping in mind that 1/4 - 1/4 = 0, so let's do that.

-3~~ = ~~-2\left[ x^2-x+\left( \cfrac{1}{2} \right)^2 ~~ - ~~\left( \cfrac{1}{2} \right)^2\right]\implies -3=-2\left(x^2-x+\cfrac{1}{4}-\cfrac{1}{4} \right) \\\\\\ -3=-2\left(x^2-x+\cfrac{1}{4} \right)+(-2)-\cfrac{1}{4}\implies -3=-2\left(x^2-x+\cfrac{1}{4} \right)+\cfrac{1}{2} \\\\\\ -3-\cfrac{1}{2}=-2\left(x^2-x+\cfrac{1}{4} \right)\implies -\cfrac{7}{2}=-2\left(x-\cfrac{1}{2} \right)^2\implies \cfrac{7}{4}=\left(x-\cfrac{1}{2} \right)^2

~\dotfill\\\\ \pm\sqrt{\cfrac{7}{4}}=x-\cfrac{1}{2}\implies \cfrac{\pm\sqrt{7}}{2}=x-\cfrac{1}{2}\implies \cfrac{\pm\sqrt{7}}{2}+\cfrac{1}{2}=x \implies \cfrac{\pm\sqrt{7}+1}{2}=x

You might be interested in
6. Consider the diagram below.
Sidana [21]

Answer:

x= 35°

I hope it's helps you

3 0
2 years ago
Read 2 more answers
Solve x2 + 6x + 7 = 0.
shtirl [24]
The answer to the question

3 0
3 years ago
Read 2 more answers
Solve -5t = 60 <br><br> 65<br> -6<br> 6<br> 55
defon
When you are asked to solve an equation, you need to isolate the variable which is t in this case. To isolate t, you would divide both sides by -5 and be left with t=-6 which is the final answer.

I hope this helps.
8 0
3 years ago
Mala ran 30 laps in week one and will increase the number of laps she runs by 2 each week. Coby runs 16 laps in week one and wil
matrenka [14]
The equations are 30+2x and 16+5x. i plug random numbers into x until you fint the correct answer. the answer is 5.

7 0
3 years ago
Evaluate: 2-4 =<br> help please
Akimi4 [234]

Answer:

-2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Sam can prepare 20wall paintings in four weeks how much time will he need to prepare 80 wall paintings
    10·2 answers
  • Choose two statements that are true fo of this expression. 5x^3- 6x^2 - 25/y + 18
    13·1 answer
  • Determine the height of the can of beans(cylinder) given the volume of the
    11·1 answer
  • HELP ME FOR BRIANETEST
    6·1 answer
  • Help plz this question is so hard for me but I hope someone can solve it plz.
    7·2 answers
  • Burgers are sold in packs of 6
    12·2 answers
  • Classify the quadrilateral using the name that best describes it.
    12·1 answer
  • Carey earns $9.75 working part time on weekends. The table below shows the amount, a, Carey earns for working h hours.
    7·2 answers
  • Jerry and Renee collect stamps. Renee collected 17 fewer than four times the number of Jerry’s stamps. Altogether, they collecte
    9·1 answer
  • Consider quadrilateral FGHJ and its image F'G'H'J'. The dilation is a(n)Immersive Reader
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!