Question

1. use the quadratic formula to solve and express in simplest form: ( x^2 - 8x = 9 )

Explanation:

Step1: Rewrite to standard quadratic form

Subtract 9 from both sides:
$x^2 - 8x - 9 = 0$

Step2: Identify a, b, c values

For $ax^2+bx+c=0$, $a=1$, $b=-8$, $c=-9$

Step3: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(-9)}}{2(1)}$

Step4: Simplify discriminant

Calculate inside the square root:
$\sqrt{64 + 36} = \sqrt{100} = 10$

Step5: Solve for x

Split into two solutions:
$x=\frac{8+10}{2}$ and $x=\frac{8-10}{2}$
Simplify each:
$x=\frac{18}{2}=9$, $x=\frac{-2}{2}=-1$

Answer:

$x=9$ and $x=-1$