Sure, let's solve the quadratic equation [tex]\( x^2 - 8x - 9 = 0 \)[/tex] and rewrite it in the form [tex]\( x^2 + bx = c \)[/tex].
First, we'll start with the given quadratic equation:
[tex]\[ x^2 - 8x - 9 = 0 \][/tex]
To rewrite it in the form [tex]\( x^2 + bx = c \)[/tex], we need to isolate the [tex]\( x \)[/tex] terms on one side and the constant term on the other side.
So, we'll move the constant term [tex]\(-9\)[/tex] to the right side of the equation:
[tex]\[ x^2 - 8x = 9 \][/tex]
Now, the equation is in the desired form [tex]\( x^2 + bx = c \)[/tex], where [tex]\( b = -8 \)[/tex] and [tex]\( c = 9 \)[/tex].
Thus, we can rewrite the initial equation as:
[tex]\[ x^2 + (-8)x = 9 \][/tex]
So, the equation [tex]\( x^2 - 8x - 9 = 0 \)[/tex] rewritten in the form [tex]\( x^2 + bx = c \)[/tex] becomes:
[tex]\[ x^2 + (-8)x = 9 \][/tex]
Now filling in the blanks:
[tex]\[ x^2 + (-8)x = 9 \][/tex]
So the solution is:
[tex]\[ x^2 - 8x = 9 \][/tex]
This completes the rewriting of the equation in the desired form.
