Question

given the equation x² - 10x = 11, solve the equation by completing the square. Be sure to put the correct + or - sign in front of your answer. x²-10x ___ = 11 ___(____)²=____so, x-5= ____ and x -5 = ____x= ____ and x=____

Answer 1

x²-10x + 25 = 11 + 25

(x-5)² = 36

so, x - 5= 6 and x - 5 = - 6

x = 11 and x = - 1

Step-by-step explanation:

To complete the square we need to take the coefficient of x, divide it by 2, and then find the square.

In this case, the coefficient of x is -10, so we need to add 25 to both sides of the equation because:

`((-10)/(2))^2=(-5)^2=25`

So, the equation is equal to:

x² - 10x = 11

x² - 10x + 25 = 11 + 25

Now, we can factorize the left side of the equation to get:

(x - 5)² = 36

So, the solution of the equation is:

`\begin{gathered} \sqrt[]{(x-5)^2}=\sqrt[]{36} \\ x-5=\pm6 \end{gathered}`

Finally:

x - 5 = 6

x - 5 + 5 = 6 + 5

x = 11

and

x - 5 = -6

x - 5 + 5 = -6 + 5

x = -1

Then, the answers are:

x²-10x + 25 = 11 + 25

(x-5)² = 36

so, x - 5= 6 and x - 5 = - 6

x = 11 and x = - 1