Answer:
(x-9) (x-5)
x = 9 x = 5
Step-by-step explanation:
find out which 2 numbers when multiplied give 45 and
when added give -14
they are -9 and -5
(x-9) (x-5)
x = 9 x = 5
Answer:
[tex]x_{1}=9, x_2=5[/tex]
Step-by-step explanation:
Recall a quadratic formula for quadratic equation [tex]ax^2+bx+c=0[/tex]: [tex]x_{1/2}=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
Notice the constant in the given equation [tex]x^2-14x+45[/tex]:
[tex]a=1, b=-14, c=45[/tex]
Substitute the values into the formula:
[tex]x_{1/2}=\frac{-(-14)\pm \sqrt{(-14)^2 -4\cdot 1\cdot 45}}{2\cdot 1}[/tex]
Calculate the values:
[tex]x_{1/2}=\frac{14\pm \sqrt{196 -180}}{2}=\frac{14\pm\sqrt{16}}{2}=\frac{14\pm 4}{2}[/tex]
It follows that there are two solutions:
[tex]x_1=\frac{14+4}{2}=\frac{18}{2}=9[/tex] and [tex]x_2=\frac{14-4}{2}=\frac{10}{2}=5[/tex].
