Module 16 – Solving Quadratic Equations by Completing the Square

Question Answer
Solve the equation by completing the square
To solve a quadratic equation by completing the square add a constant to both sides of the equation so that the remaining trinomial is a perfect square trinomial.
The coefficient of x^2 term of the quadratic equation must be equal to 1 in order to determine the constant to be added to both sides of the equation.
Is the leading coefficient equal to 1?


yes or no?

If you answered yes, you are correct!! :))
Rewrite the equation with the constant by itself on the right side of the equation.
Subtract 22 from both sides


Now take 1/2 of the numerical coefficient of the x-term and square it.
x term is equal to 10x
1/2* (10) = 5
now square it
(5)^2 = 25
Add the constant 25 to both sides of the equation to form a perfect square trinomial on the left side of the equation as the square of a binomial
Now add 25 to both sides…


Now factor the left side


It should look like this:

(x+5)^2= -22+25

Now, simplify the right side of the equation
(x+5)^2= -22+25
Which should look like this:

(x+5)^2= 3

The square root property is stated as…. If x^2=a where a is a real number then x=+/-va
Use the square root property. Remember that the value on the right can be positive or negative. Solve for x. (x+5)^2 = 3
x+5=v3 or x+5= -v3

x= -5+v3, -5-v3

Congrats you made it through!! 🙂