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 Mathematics
[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 squareSolving (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
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
[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
(n- 2/3)²Step-by-step explanation:Perfect square trinomial is: a²+2ab+b²= (a+b)²We have:n² - 4n/3It can be put as:n² -2×n×2/3Here we consider n = a and -2/3 = b, thenb²= (-2/3)²= 4/9Now we add 4/9 to a given binomial to make it perfect square:n² - 2×n×3/2 + 4/9= (n- 2/3)²So, added 4/9 and got a perfect square (n- 2/3)²Reply
(y+5)²Step-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+25Finally, using the mentioned rule, the binomial square for that equation is (y+5)²Reply
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
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 youReply
[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]
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].
[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]
(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
(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
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]
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