+0  
 
0
81
3
avatar

If \[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $a.$

 

If \[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $c.$

 

If you complete the square on the equation \[x^2 + 10x = 9,\]you will get an equation of the form "$(x + r)^2 = c$".

 

For what real values of $a$ is $x^2 + ax + 25$ the square of a binomial? If you find more than one, then list the values separated by commas.

 

Find all real solutions to\[100x^2+20x+1=16.\]

 

Find all real values of $x$ that satisfy the equation $(x^2 - 82)^2 = 324$. If you find more than one, then list the values separated by commas.

 

Find the smallest real value of $x$ such that $x^2+6x + 9 = 24$.

 

Find the roots of $x^2 + 12x + 36 + 25 = 0.$

 Dec 20, 2020
 #3
avatar+112038 
+1

I think that presentation is confusing too!

 

Try expanding this    \((x+7)^2\)  and you will get     \(x^2+17x+49 \)

Do it to make sure you know how and to check I did it right.

 

so I have    \(x^2+14x+49=(x+7)^2\)

 

Notice if I half the 14 I get 7

If I square the 7 I git 49

so

 

\(x^2+14x+(\frac{14}{2})^2=(x+\frac{14}{2})^2\)

\(​​​​\)

If there is no number in front of the x^2 except for an invisible 1 then this will always be true.

 

Consider your example:

 

\(x^2 - 7x + c = (x + a)^2\)

 

c will be  half of -7

a will be (half of -7) squared.

 

So you complete this bit for me please.

 Dec 20, 2020

26 Online Users