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
In which function does an increase of 1 in quantity x correspond to an increase of 8 in
OLga [1]

Answer:

C. y = 8x

Step-by-step explanation:

When x = 1

y = 8(1) = 8

when x = 2

y = 8(2) = 16

x increased by 1

y increased by 8

8 0
2 years ago
What percent is equivalent to 18/30
FrozenT [24]

18 / 30 =

60 percent


4 0
3 years ago
Read 2 more answers
15 POINTS‼️‼️‼️<br><br> Part B: Solve for x. Show your work.
Musya8 [376]

Answer:

Step-by-step explanation:

A straight line adds up to 180 degrees, therefore 3x+6x = 180

9x = 180

x = 20

7 0
3 years ago
What is 18049 divided by 14
yawa3891 [41]
Simply divide with your calculator

18049/14 ≈ 1289.214

 ≈ 1289.214
6 0
3 years ago
The systematic repayment of a loan through a set number of payments at a
Romashka-Z-Leto [24]

Answer:

D

Step-by-step explanation:

Amortization is the systematic repayment or writing off a loan through a number of payments at a specific interest rate.

6 0
3 years ago
Other questions:
  • Jackson runs 7/8 mile in 1/2 hour. How many miles does Jackson run in 1 hour? Show work. Please answer this I don’t get it!!
    9·1 answer
  • Solve the equation. If necessary, round your answer to the nearest tenth.
    10·2 answers
  • What is 13/20 times 60/x
    15·1 answer
  • Write the equation of the line with the points (6, 6) and (-2, 1) in slope-intercept form
    6·2 answers
  • Find the value of x.<br><br>Please help!!​
    5·2 answers
  • There are 20 nickels in a dollar
    8·1 answer
  • Which of the following functions maps 3 to -5?
    14·1 answer
  • Which choice is a correct congruence statement for the triangles?
    15·1 answer
  • Mr. Jansen opened a savings account with an initial deposit of $720 and will not make any additional deposits or withdrawals. Th
    14·2 answers
  • Bc
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!