Beginning and Intermediate Algebra - Wallace Math Courses ...

x =
Example 468.
√
30 ± 900 + 1100
50 √
30 ± 2000
x =
50
30 ± 20 5
x = √
50
3 ± 2 5
x = √
5
Evaluate addition inside root
Simplify root
Reduce fraction by dividing each term by 10
Our Solution
3x 2 + 4x+8=2x 2 +6x − 5 First set equation equal to zero
− 2x 2 − 6x+5 − 2x 2 − 6x + 5 Subtract2x 2 and 6x and add5
x2 − 2x + 13 =0 a =1, b = − 2, c=13, use quadratic formula
x = 2 ± ( − 2)2 �
− 4(1)(13)
Evaluate exponent and multiplication
2(1)
√
2 ± 4 − 52
x = Evaluate subtraction inside root
√2
2 ± − 48
x = Simplify root
2
2 ± 4i 3
x = √
Reduce fraction by dividing each term by 2
2
x = 1 ± 2i 3
√
Our Solution
When we use the quadratic formula we don’t necessarily get two unique answers.
We can end up with only one solution if the square root simplifies to zero.
Example 469.
4x2 − 12x +9=0 a = 4,b=−12, c=9, use quadratic formula
x = 12 ± ( − 12)2 �
− 4(4)(9)
Evaluate exponents and multiplication
2(4)
√
12 ± 144 − 144
x = Evaluate subtraction inside root
8
12 ± 0
x = √
Evaluate root
8
12 ± 0
x = Evaluate ±
8
x = 12
Reduce fraction
8
x= 3
Our Solution
2
345