Precalculus help! ASAP quadratic equations

Question

solve the following:
a) 3(2z+3)²-9(2z+3)-30 = 0
b)0.49k²-36m²= 0

Answer 1

 

a) 3(2z+3)²-9(2z+3)-30=0

divide both sides by 3

(2z+3)²-3(2z+3)-10=0

let n=2z+3

n²-3n-10=0

factor

(n-5)(n+2)=0

n-5=0

n=5

but n=2z+3, so...

2z+3=5

2z=2

z=1

n+2=0

n=-2

but n=2z+3

2z+3=-2

2z=-5

z=-5/2

 

b) 0.49k²-36m²=0

factor

(0.7k-6m)(0.7k+6m)=0

0.7k-6m=0

0.7k=6m

7k=60m

k=60m/7, or

m=7k/60

0.7k+6m=0

0.7k=-6m

7k=-60m

k=-60m/7, or

m=7k/-60