Question

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

Answer 1

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

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

Answer 2

$45=x(14-x)\\ \\45=14x-x^2\\ \\x^2-14x+45=0\\ \\\Delta = b^{2}-4ac = (-14)^{2}-4*1* 45=196-180=16 \\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{14- \sqrt{16}}{2}=\frac{14-4}{2}= \frac{12}{2}=6\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{14+\sqrt{16}}{2}=\frac{14+4}{2}= \frac{18}{2}=9$