5.7: Solving Quadratics Using Square Roots
Mrs. Garber draws a square on the board and writes the equation
Watch This
Khan Academy: Solving Quadratics by Square Roots
Guidance
Now that you are familiar with square roots, we will use them to solve quadratic equations. Keep in mind, that square roots cannot be used to solve every type of quadratic. In order to solve a quadratic equation by using square roots, an
Example A
Solve
Solution: Start by isolating the
At this point, you can take the square root of both sides.
Notice that
Check:
Example B
Solve
Solution: Isolate
Example C
Solve
Solution: In this example,
Now that the square root is gone, add 5 to both sides.
Intro Problem Revisit To find s, isolate
Therefore the length of the square's side is
Guided Practice
Solve the following quadratic equations.
1.
2.
3.
Answers
1. Isolate
2. Combine all like terms, then isolate
3. Isolate what is being squared, take the square root, and then isolate
Practice
Solve the following quadratic equations. Reduce answers as much as possible. No decimals.

x2=144 
5x2−4=16 
8−10x2=−22 
(x+2)2=49 
6(x−5)2+1=19 
34x2−19=26 
x2−12=36−2x2 
9−x23=−33 
−4(x+7)2=−52 
2(3x+4)2−5=45 
13(x−10)2−8=16 
(x−1)26−83=72
Use either factoring or solving by square roots to solve the following quadratic equations.

x2−16x+55=0 
2x2−9=27 
6x2+23x=−20  Writing Write a set of hints that will help you remember when you should solve an equation by factoring and by square roots. Are there any quadratics that can be solved using either method?
 Solve
x2−9=0 by factoring and by using square roots. Which do you think is easier? Why?  Solve
(3x−2)2+1=17 by using square roots. Then, solve3x2−4x−4=0 by factoring. What do you notice? What can you conclude?  Real Life Application The aspect ratio of a TV screen is the ratio of the screen’s width to its height. For HDTVs, the aspect ratio is 16:9. What is the width and height of a 42 inch screen TV? (42 inches refers to the length of the screen’s diagonal.) HINT: Use the Pythagorean Theorem. Round your answers to the nearest hundredth.

Real Life Application When an object is dropped, its speed continually increases until it reaches the ground. This scenario can be modeled by the equation \begin{align*}h=16t^2+h_0\end{align*}, where \begin{align*}h\end{align*} is the height, \begin{align*}t\end{align*} is the time (in seconds), and \begin{align*}h_0\end{align*} is the initial height of the object. Round your answers to the nearest hundredth.
 If you drop a ball from 200 feet, what is the height after 2 seconds?
 After how many seconds will the ball hit the ground?
Notes/Highlights Having trouble? Report an issue.
Color  Highlighted Text  Notes  

Please Sign In to create your own Highlights / Notes  
Show More 
Image Attributions
Here you'll use the properties of square roots to solve certain types of quadratic equations.