We previously learned how to solve a quadratic equation using factoring, and completing the square. Factoring is simple, but doesn’t always work. Completing the square works for all scenarios, but is very tedious. The quadratic formula allows us to quickly and easily solve any quadratic equation. This method allows us to plug in for the given parameters, simplify, and gain our solution.

Test Objectives
• Demonstrate the ability to place a quadratic equation in standard form
• Demonstrate the ability to solve a quadratic equation using the quadratic formula
• Demonstrate the ability to solve a quadratic equation with a complex solution

#1:

Instructions: Solve each using the quadratic formula.

a) $$-8m^2 - 8m = -18$$

b) $$3n^2 - 5 = 0$$

#2:

Instructions: Solve each using the quadratic formula.

a) $$5p^2 - 6p = 32$$

b) $$-5n^2 = -80$$

#3:

Instructions: Solve each using the quadratic formula.

a) $$2x^2 - 28 = -x$$

b) $$8n^2 + 2 = -1$$

#4:

Instructions: Solve each using the quadratic formula.

a) $$-10b^2 - b - 17 = -10$$

b) $$4a^2 + 10a - 16 = -5$$

#5:

Instructions: Solve each using the quadratic formula.

a) $$3x^2 + 8 = -7x - 5x^2$$

b) $$5r^2 + 9r = r^2 - 8$$

Written Solutions:

#1:

Solutions:

a) $$m = \frac{-1 \pm \sqrt{10}}{2}$$

b) $$n = \frac{\pm \sqrt{15}}{3}$$

#2:

Solutions:

a) $$p = \frac{16}{5} \hspace{.5em} or \hspace{.5em} p = -2$$

b) $$n = 4 \hspace{.5em} or \hspace{.5em} n = -4$$

#3:

Solutions:

a) $$x = \frac{7}{2} \hspace{.5em} or \hspace{.5em} x = -4$$

b) $$n = \frac{\pm\hspace{.25em} i\sqrt{6}}{4}$$

#4:

Solutions:

a) $$b = \frac{-1 \pm 3i\sqrt{31}}{20}$$

b) $$a = \frac{-5 \pm \sqrt{69}}{4}$$

#5:

Solutions:

a) $$x = \frac{-7 \pm 3i\sqrt{23}}{16}$$

b) $$r = \frac{-9 \pm i\sqrt{47}}{8}$$