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# Module 16

### Module 16 - Solving Quadratic Equations by Completing the Square

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=+/-√a
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+=/-√3 x+5=√3 or x+5= -√3 x= -5+√3, -5-√3 Congrats you made it through!! :)
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