Question

Whats the answer to 45=x(14-x)

Answer 1

`45=x(14-x)\\\\45=x\cdot14-x\cdot x\\\\45=14x-x^2\\\\-x^2+14x-45=0\\\\a=-1;\ b=14;\ c=-45\\\\\Delta=b^2-4ac;\ \Delta=14^2-4\cdot(-1)\cdot(-45)=196-180=16\\\\x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\x_1=(-14-√(16))/(2\cdot(-1))=(-14-4)/(-2)=(-18)/(-2)=9\\\\x_2=(-14+√(16))/(2\cdot(-1))=(-14+4)/(-2)=(-10)/(-2)=5`


`Answer:x=9\ or\ x=5.`

Answer 2

`45=x(14-x)\\ \\45=14x-x^2\\ \\x^2-14x+45=0\\ \\\Delta = b^(2)-4ac = (-14)^(2)-4*1* 45=196-180=16 \\ \\x_(1)=(-b-√(\Delta ))/(2a) =(14- √(16))/(2)=(14-4)/(2)= (12)/(2)=6\\ \\x_(2)=(-b+√(\Delta ))/(2a) =(14+√(16))/(2)=(14+4)/(2)= (18)/(2)=9`