Find exact solutions to each of the following equations

Question

Find exact solutions to each of the following equations

 

1. 18-9x-2x^2=0

 

2. x^4-7x^2-144=0

 

3. 12x^2-7x=12

 

4. x^2-10x+34=0

Answer 1

solve by factoring:

 

1. (2x-3)(-x-6) = -2x^2 - 9x + 18 check

thus x = -6, x = 3/2

 

2. (x^2+9)(x^2-16) = x^4-7x^2-144 check

thus x = +3, -3; x = +4, -4

 

3. (4x+3)(3x-4) = 0

thus x = -3/4, 4/3

 

4. solve by using quadratic formula [-b+-sqrt(b^2-4ac)]/2a

where b = -10, a = 1, c = 34

[-10+-sqrt(100-136)]/2 = -5+-3i

x = -5+3i, -5-3i