We previously spoke about quadratic equations and learned how to solve a quadratic equation when it is factorable. Here we begin to develop techniques to solve any quadratic equation, whether it is factorable or not. Specifically, we will focus on solving simple quadratic equations using the square root property.

Test Objectives
• Demonstrate a general understanding of the square root property
• Demonstrate the ability to solve a quadratic equation of the form: x2 = k
• Demonstrate the ability to solve a quadratic equation of the form: (x + a)2 = k
Square Root Property Practice Test:

#1:

Instructions: solve each equation

$$a)\hspace{.2em}17x^2 + 10=129$$

$$b)\hspace{.2em}18x^2 + 1=3403$$

#2:

Instructions: solve each equation

$$a)\hspace{.2em}10x^2 + 5=995$$

$$b)\hspace{.2em}17x^2 + 6=-368$$

#3:

Instructions: solve each equation

$$a)\hspace{.2em}14x^2 + 9=65$$

$$b)\hspace{.2em}15x^2 + 3=-147$$

#4:

Instructions: solve each equation

$$a)\hspace{.2em}13 - 15x^2=-2927$$

$$b)\hspace{.2em}20 + 400x^2=56$$

#5:

Instructions: solve each equation

$$a)\hspace{.2em}2(x - 9)^2=288$$

$$b)\hspace{.2em}4(3x - 5)^2=-500$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}x=\pm \sqrt{7}$$

$$b)\hspace{.2em}x=\pm 3\sqrt{21}$$

#2:

Solutions:

$$a)\hspace{.2em}x=\pm 3\sqrt{11}$$

$$b)\hspace{.2em}x=\pm i\sqrt{22}$$

#3:

Solutions:

$$a)\hspace{.2em}x=\pm 2$$

$$b)\hspace{.2em}x=\pm i\sqrt{10}$$

#4:

Solutions:

$$a)\hspace{.2em}x=\pm 14$$

$$b)\hspace{.2em}x=\pm \frac{3}{10}$$

#5:

Solutions:

$$a)\hspace{.2em}x=-3,21$$

$$b)\hspace{.2em}x=\frac{5 \pm 5i \sqrt{5}}{3}$$