Question

Find the solutions(s) to 9x^2-54x+0

Answer 1

x = 6

x = 0

• As shown, there are 2 values for x. The question is why, which we will go over in the explanation part.

Explanation:

identify the coefficients

`9x^2-54x=0\\a=9\\b=-54\\c=0`

coefficient a = 1

`9x^2-54x=0\\9/9x^2-54x/9=0/9\\x^2-6x=0\\\rightarrow a=1\\\rightarrow b=-6\\\rightarrow c=0`

complete the square

`b=-6\\((b)/(2))^2=((-6)/(2))^2\\((x)/(y))^2=(x^2)/(y^2)\\=((-6)/(2))^2=(-6^2)/(2^2)\\(-6^2)/(2^2)=(36)/(4)\\36 / 4=9\\\\\downarrow\\\\x^2-6x=0\\x^2-6x+9=0+9\\x^2-6x+9=9\\(b)/(2)\\(b)/(2)=(-6)/(2)\\(b)/(2)=(\left(-3\cdot 2\right))/(\left(1\cdot 2\right))\\(b)/(2)=-3\\x^2-6x+9=9\\(x-3)^2=9\\`

solve for x

`(x-3)^2=9\\√((x-3)^2)=√(9)\\x-3=+-√(9)\\x-3+3=3+-√(9)\\x=3+-√(9)\\x=3+-3\\x_1=6\\x_2=0`

≡ In the end, you have 2 values for x, because you can either subtract 3 by 3 or add 3 by 3 to get six or zero.