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Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. c^2+2c

Posted on October 22, 2021 By Hannahkharel2 7 Comments on Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. c^2+2c

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. c^2+2c

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Comments (7) on “Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. c^2+2c”

  1. abolton04 says:
    October 23, 2021 at 9:23 am

    [tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]

    [tex](n + \frac{5}{4})^2[/tex]

    Step-by-step explanation:

    Given

    [tex]n^2 + \frac{5}{2}n[/tex]

    Required

    (a) Make a perfect square trinomial

    (b) Write as binomial square

    Solving (a)

    Let the missing part of the expression be k;

    This gives

    [tex]n^2 + \frac{5}{2}n + k[/tex]

    To solve for k, we need to square half the coefficient of n;

    i.e. Since the coefficient of n is [tex]\frac{5}{2}[/tex], then

    [tex]k = (\frac{1}{2} * \frac{5}{2})^2[/tex]

    [tex]k = (\frac{5}{4})^2[/tex]

    [tex]k = \frac{25}{16}[/tex]

    Hence;

    [tex]n^2 + \frac{5}{2}n + k[/tex] = [tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]

    Solving (b)

    [tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]

    Expand [tex]\frac{5}{2}n[/tex]

    [tex]n^2 + \frac{5}{4}n+ \frac{5}{4}n + \frac{25}{16}[/tex]

    Factorize

    [tex]n(n + \frac{5}{4})+ \frac{5}{4}(n + \frac{5}{4})[/tex]

    [tex](n + \frac{5}{4})(n + \frac{5}{4})[/tex]

    [tex](n + \frac{5}{4})^2[/tex]

    Hence:

    [tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex] = [tex](n + \frac{5}{4})^2[/tex]

    Reply
  2. bapefer498 says:
    October 23, 2021 at 11:03 am

    Perfect square trinomial: [tex]n^2+n+\dfrac{1}{4}[/tex]

    Binomial squared: [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].

    Step-by-step explanation:

    The given expression is [tex]n^2+n.[/tex]

    Here coefficient of n is 1.

    Now, find square of half of coefficient of n.

    [tex]\left(\dfrac{1}{2}\times 1\right)^2=\dfrac{1}{4}[/tex]

    Now, add [tex]\dfrac{1}{4}[/tex] in the expression to make it perfect square trinomial.

    [tex]n^2+n+\dfrac{1}{4}[/tex]

    [tex]\Rightarrow n^2+n+\left(\dfrac{1}{2}\right)^2[/tex]

    [tex]\Rightarrow \left(n+\dfrac{1}{2}\right)^2[/tex]      [tex]\because (a+b)^2=a^2+2ab+b^2[/tex]

    Therefore, perfect square trinomial is [tex]n^2+n+\dfrac{1}{4}[/tex] and binomial squared is [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].

    Reply
  3. emilycolley2 says:
    October 23, 2021 at 12:41 pm

     [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

    Step-by-step explanation:

    [tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

    Reply
  4. tireekkimble5 says:
    October 23, 2021 at 9:47 pm

    (n- 2/3)²

    Step-by-step explanation:

    Perfect square trinomial is: a²+2ab+b²= (a+b)²

    We have:

    n² - 4n/3

    It can be put as:

    n² -2×n×2/3

    Here we consider n = a and -2/3 = b, then

    b²= (-2/3)²= 4/9

    Now we add 4/9 to a given binomial to make it perfect square:

    n² - 2×n×3/2 + 4/9= (n- 2/3)²

    So, added 4/9 and got a perfect square (n- 2/3)²

    Reply
  5. LtPeridot says:
    October 23, 2021 at 10:27 pm

    (y+5)²

    Step-by-step explanation:

    Every perfect square trinomial, completes the rule:

    (a+b)²=(a²+2ab+b²)

    Let's complete the PST:

    (a) would be the square root of y², which is y.

    (b) would be a number that multiplied by 2y gives us 10y, which is 5.

    Our perfect square trinomial is y²+10y+25

    Finally, using the mentioned rule, the binomial square for that equation is (y+5)²

    Reply
  6. ComicSans10 says:
    October 24, 2021 at 2:00 am

    Take the coefficient of ''n'', divide it by 2, and raise it to the second power;

    [tex]n^2+n+(\frac{1}{2})^2[/tex]

    [tex]n^2+n+\frac{1}{4}=0[/tex]

    [tex]=(n+\frac{1}{2} )^2[/tex]

    Reply
  7. jadav350 says:
    October 24, 2021 at 3:13 am

    Step-by-step explanation:

    Hello, please consider the following.

    [tex]q^2-\dfrac{1}{4}q=q^2-2\cdot \dfrac{1}{8}\cdot x=(q-\dfrac{1}{8})^2-\dfrac{1}{8^2}\\\\=\boxed{(q-\dfrac{1}{8})^2-\dfrac{1}{64}}\\\\\text{ We need to add } \dfrac{1}{64} \text{ to complete the square.}\\\\[/tex]

    [tex]\Large \boxed{\sf \ \ q^2-\dfrac{1}{4}q+\dfrac{1}{64}=(q-\dfrac{1}{8})^2 \ \ }[/tex]

    Hope this helps.

    Do not hesitate if you need further explanation.

    Thank you

    Reply

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