To solve the quadratic equation $x^2 - 18x = 40$, we first need to rewrite it in standard form:

$x^2 - 18x - 40 = 0$

Now, we can solve this equation using the quadratic formula, which is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For the equation $x^2 - 18x - 40 = 0$, the coefficients are:

• $a = 1$
• $b = -18$
• $c = -40$

Substitute these values into the quadratic formula:

$x = \frac{-(-18) \pm \sqrt{(-18)^2 - 4(1)(-40)}}{2(1)}$

Simplify the expression:

$x = \frac{18 \pm \sqrt{324 + 160}}{2}$

$x = \frac{18 \pm \sqrt{484}}{2}$

$x = \frac{18 \pm 22}{2}$

Now, solve for the two possible values of $x$:

1. $x = \frac{18 + 22}{2} = \frac{40}{2} = 20$
2. $x = \frac{18 - 22}{2} = \frac{-4}{2} = -2$

So the solutions are $x = 20$ and $x = -2$.

Correct choice:

• B. $x = 20$ and $x = -2$

Would you like further explanation or have any questions? Here are some related problems to try:

1. How do you factor a quadratic equation when the quadratic formula is not required?
2. Can you derive the quadratic formula starting from the general form $ax^2 + bx + c = 0$?
3. What is the discriminant of the quadratic equation $x^2 - 18x - 40 = 0$ and what does it tell you?
4. How can completing the square be used to solve the quadratic equation $x^2 - 18x = 40$?
5. How would the solution change if the equation were $x^2 - 18x + 40 = 0$?

Tip: When solving quadratic equations, double-check your discriminant calculation to ensure it determines the correct nature of the roots!