Question

What is x^2-9x+4=0? please help.. i’m using this method: (x+b)^2-b^2=x^2+2bx

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

x² - 9x + 4 = 0 ( subtract 4 from both sides )

x² - 9x = - 4

Using the method of completing the square

Add ( half the coefficient of the x- term )² to both sides

x² +2 (- $\frac{9}{2}$)x + $\frac{81}{4}$ = - 4 + $\frac{81}{4}$

(x - $\frac{9}{2}$)² = $\frac{65}{4}$

Take the square root of both sides

x - $\frac{9}{2}$ = ± $\sqrt{\frac{65}{4} }$ = ± $\frac{1}{2}$$\sqrt{65}$

Add $\frac{9}{2}$ to both sides

x = $\frac{9}{2}$ ± $\frac{1}{2}$$\sqrt{65}$ ← exact solutions