Answer:
x = 7 and x = -1
Explanation:
The initial equation is:
3x²-21=18x
So, let move the terms with x to one side and the constant terms to the other side as:
3x² - 18x = 21
Now, we can divide by 3:
[tex]\begin{gathered} \frac{3x^2-18x}{3}=\frac{21}{3} \\ x^2-6x=7 \end{gathered}[/tex]Now, to complete the square, we need to find a value that is equal to the square of the half of -6, the number beside the x, so the value is:
[tex](\frac{-6}{2})^2=(-3)^2=9[/tex]Then, we add 9 to both sides of the equation as:
[tex]\begin{gathered} x^2-6x+9=7+9 \\ (x-3)^2=16 \end{gathered}[/tex]So, solving for x, we get:
[tex]\begin{gathered} \sqrt[]{(x-3)^2}=\sqrt[]{16} \\ x-3=4\to x=4+3=7 \\ or \\ x-3=-4\to x=-4+3=-1 \end{gathered}[/tex]Therefore, the solutions are x = 7 and x = -1
