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