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 $x^2 + 12x + 36 + 25 = 0.$

Guest Dec 20, 2020

#3**+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.

Melody Dec 20, 2020