Question

What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?

Answer 1

`2x^2+16x-9=0\ \ \ |+9\\\\2x^2+16x=9\ \ \ |:2\\\\x^2+8x=4.5\\\\x^2+2x\cdot4=4.5\ \ \ |+4^2\\\\\underbrace{x^2+2x\cdot4+4^2}_((a+b)^2=a^2+2ab+b^2)=4.5+4^2\\\\(x+4)^2=20.5\to x+4=\pm√(20.5)\\\\x+4=-\sqrt{(205)/(10)}\ \vee\ x+4=\sqrt{(205)/(10)}\\\\x+4=-\sqrt{(2050)/(100)}\ \vee\ x+4=\sqrt{(2050)/(10)}\\\\x+4=-(√(25\cdot82))/(10)\ \vee\ x+4=(√(25\cdot82))/(10)\\\\x=(-40-5√(82))/(10)\ \vee\ x=(-40+5√(82))/(10)`