2.2c Solving Quadratic Equations – Quadratic Formula

The quadratic equation a x 2 + b x + c = 0 can be solved by using the quadratic formula
b ± b 2 4 a c 2 a
Example 
Use the quadratic formula to find the solutions of the following equations.
a. x 2 + 5 x 24 = 0
b. x ( x + 4 ) = 10
Answer
a. For the equation x 2 + 5 x 24 = 0
a = 1, b = 5, c = -24
x = b ± b 2 4 a c 2 a x = ( 5 ) ± ( 5 ) 2 4 ( 1 ) ( 24 ) 2 ( 1 ) x = 5 ± 121 2 x = 8  or  x = 3
b.
x ( x +  4 )   =  10 x 2 + 4 x 10 = 0 a = 1 ,    b = 4 ,    c = 10 x = b ± b 2 4 a c 2 a x = ( 4 ) ± ( 4 ) 2 4 ( 1 ) ( 10 ) 2 ( 1 ) x = 4 ± 56 2 x = 1.742  or  x = 5.742

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