Solving Quadratic Equations by Completing the Square

x = -5 ± √30

x = 5 ± √30

x = 30 ± √5

x = -30 ± √5

X = 6 + √41 or  6 − √41

X= 35 or 47

X = −6 + √41 or  −6 − √41

X = √35 or √47

$$\left(x-\frac{3}{2}\right)^2=\frac{5}{4}$$  

$$\left(x-\frac{1}{6}\right)^2=\frac{1}{3}$$  

$$\left(x+\frac{1}{6}\right)^2=\frac{5}{3}$$  

$$\left(x+\frac{3}{2}\right)^2=\frac{13}{4}$$  

8

64

16

4

256

Take half of 10 and square it.

Add 25 to both sides.

Solve the perfect square trinomial

Take the square root of both sides

Solve for x to get a solution.

Take half of -9 and add to both sides.

Divide all terms by 10

Set equal to zero.

8

64

16

4

256

$$\left(x-\frac{3}{2}\right)^2=\frac{5}{4}$$  

$$\left(x-\frac{1}{6}\right)^2=\frac{1}{3}$$  

$$\left(x+\frac{1}{6}\right)^2=\frac{5}{3}$$  

$$\left(x+\frac{3}{2}\right)^2=\frac{13}{4}$$