# Download Notes Over 5.6 Solving a Quadratic Equation with Two Real Solutions

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```Notes Over 5.6
Quadratic Formula
The solutions of the quadratic equation
2
y  ax  bx  c
are given by the Quadratic Formula:
b  b  4ac
2
2a
Notes Over 5.6
Solving a Quadratic Equation with Two Real Solutions
Use the quadratic formula to solve the equation.
1. x  9 x  5  0
2
  b9  
 b9   4 1a  5c 
21
a
2
9  81 20 9  61

2
2
Notes Over 5.6
Solving a Quadratic Equation with Two Real Solutions
Use the quadratic formula to solve the equation.
2. 5 x  3x  1  0
2
  b3  

b3   4 a5 c1
2  a5 
 3  9  20
10
2
 3  29

10
Notes Over 9.5
Solving a Quadratic Equation with Two Real Solutions
Use the quadratic formula to solve the equation.
3.  x  2 x  4  0
2
  b2  

b2   4 a1 4c
2  a1 
2
 2  4  16
2

 2  20

2
22 5

 1 5
2
Notes Over 5.6
Solving a Quadratic Equation with One Real Solution
Use the quadratic formula to solve the equation.
4. x  6 x  9  0
2
  b6  
 b6   4 1a  9c 
21
a
2
6  36 36 6
 3
2
2
Notes Over 5.6
Solving a Quadratic Equation with One Real Solution
Use the quadratic formula to solve the equation.
5. x  4 x  4  0
2
  b4  

b4   4 1
a  4c 
21
a
2
 4  16  16  4

 2
2
2
Notes Over 5.6
Solving a Quadratic Equation with One Real Solution
Use the quadratic formula to solve the equation.
6. x  10 x  25  0
2
  10
b 
 10
b   4 1
a 25
c
21
a
2
 10  100 100  10

 5
2
2
Notes Over 5.6
Solving a Quadratic Equation with Two Imaginary Solution
Use the quadratic formula to solve the equation.
7. x  6 x  10
x  6 x  10  0
2
  b6  
2
 b6   4 1a 10
c
21
a
6 4
2
6  36 40 
2
2 36  2i

 3i
2
Notes Over 5.6
Solving a Quadratic Equation with Two Imaginary Solution
Use the quadratic formula to solve the equation.
8. x   x  1
x  x 1  0
2
  b1  

2
b1   4 1
a  1c 
21
a
2
 1  3
 1 1  4 
2
2 1 i 3

2
Notes Over 5.6
Solving a Quadratic Equation with Two Imaginary Solution
Use the quadratic formula to solve the equation.
9. x  2 x  3  0
2
  b2  
2
 b2   4 1a  3c 
21
a
2  8
2
4  12 
2
2
2  2i 2

 1 i 2
2
Notes Over 5.6
```
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