Module 16 – Solving Quadratic Equations by Completing the Square

Question Answer
Solve the equation by completing the square
x^2+10x+22=0
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?

x^2+10x+22=0

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.
x^2+10x+22=0
Subtract 22 from both sides

X^2+10x=-22

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
x^2+10x=-22
Now add 25 to both sides…

x^2=10x=25=-22+25

Now factor the left side

x^2=10x=25=-22+25

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
x+5=v3 or x+5= -v3

x= -5+v3, -5-v3

Congrats you made it through!! 🙂