1. 2.13 Warm Up x² - 2x + 15 = 0; 3 x² + 3x – 4 = 0; 1
Determine whether the given value is a solution of the equation.
x² - 2x + 15 = 0; 3
x² + 3x – 4 = 0; 1
x² - 4x – 12 = 0; 2

2. 2.13 Using Square Roots to Solve Quadratic Equations

3. All positive real numbers have 2 square roots
Positive square root (principle square root)
Negative square root
Radicand: number or expression inside the radical symbol
Perfect square: squared integer
If there is no b, you can isolate the x2 and then solve using square roots.

4. Solve quadratic equations
EXAMPLE 1
Solve quadratic equations
Solve the equation.
a. 2x2 = 8
SOLUTION
a. 2x2 = 8
Write original equation.
x2 = 4
Divide each side by 2.
x = ± 4 = ± 2 
Take square roots of each side.
Simplify.
The solutions are –2 and 2.
ANSWER

5. Solve quadratic equations
EXAMPLE 1
Solve quadratic equations
b. m2 – 18 = – 18
Write original equation.
m2 = 0
Add 18 to each side.
m = 0
The square root of 0 is 0.
ANSWER
The solution is 0.

6. Solve quadratic equations
EXAMPLE 1
Solve quadratic equations
c. b = 5
Write original equation.
b2 = – 7
Subtract 12 from each side.
ANSWER
Negative real numbers do not have real square roots.
So, there is no real solution.

7.  EXAMPLE 2 Take square roots of a fraction Solve 4z2 = 9. SOLUTION
Write original equation.
z2 = 9 4
Divide each side by 4.
z = ±  9 4
Take square roots of each side.
z = ± 3 2
Simplify.
The solutions are – and 3 2

8. Approximate solutions of a quadratic equation
EXAMPLE 3
Approximate solutions of a quadratic equation
Solve 3x2 – 11 = 7. Round the solutions to the nearest
hundredth.
SOLUTION
3x2 – 11 = 7
Write original equation.
3x2 = 18
Add 11 to each side.
x2 = 6
Divide each side by 3.
x = ± 6 
Take square roots of each side.
The solutions are about – 2.45 and about 2.45.

9. EXAMPLE 1
GUIDED PRACTICE
Solve quadratic equations
for Examples 1,2 and 3
Solve the equation.
1. c2 – 25 = 0
ANSWER
–5, 5.
w = – 8
ANSWER
no solution
x = 11
ANSWER

10. EXAMPLE 1
GUIDED PRACTICE
Solve quadratic equations
for Examples 1,2 and 3
Solve the equation.
ANSWER 4 5 – ,
x2 = 16
ANSWER 10 3 – ,
m2 = 100
b = 0
ANSWER
no solution
Solve the equation. Round the solutions to the nearest hundredth.
ANSWER
– 3.16, 3.16
7. x2 + 4 = 14
k2 – 1 = 0
ANSWER
– 0.58, 0.58
p2 – 7 = 2
ANSWER
– 2.12, 2.12

11. Solve a quadratic equation
EXAMPLE 4
Solve a quadratic equation
Solve 6(x – 4)2 = 42. Round the solutions to the nearest
hundredth.
6(x – 4)2 = 42
Write original equation.
(x – 4)2 = 7
Divide each side by 6.
x – 4 = ± 7 
Take square roots of each side. 7 
x = 4 ±
Add 4 to each side.
ANSWER
The solutions are and 4 – 7 

12. EXAMPLE 1
GUIDED PRACTICE
Solve quadratic equations
for Examples 4 and 5
Solve the equation. Round the solution to the nearest hundredth if necessary.
(x – 2)2 = 18
ANSWER
–1, 5
(q – 3)2 = 28
ANSWER
0.35, 5.65
(t + 5)2 = 24
ANSWER
–7.83, –2.17