Solving By Completing The Square (When a=1)

This lesson covers:

  1. How to use the 'complete the square' technique to solve quadratic equations
  2. E.g. 'By completing the square solve x2 + 6x + 8 = 0'

Quadratic equations such as 'x2 + 6x + 8 = 0' can be solved in multiple ways including:

  1. Factorising the equation into two brackets
  2. Using the quadratic formula
  3. Completing the square. 


In this lesson we practise the completing the square technique. This involves two steps:

1  Completing the square to get something in the form '(x + p)2 + q = 0'

2Then solving to find x by rearranging to get x by itself.


In the first few questions we'll give you the equation in the form  '(x + p)2 + q = 0' so that all you have to do is rearrange for x. Then in later questions we'll start from the original quadratic, and you'll have to do both steps. 


Completing the square for 'x2 + 6x = 0' gives:

(x+3)2−9=0

Hence solve the equation to find x.

x=0 and x=−6
x=3 and x=−6
x=0 and x=9
x=3 and x=0

0

/

1

Completing the square for 'x2 - 6x - 3 = 0' gives:

(x−3)2−12=0

Hence solve the equation to find x.

x=3±2√3
x=3±3√2
x=±2√3−3

0

/

1

Completing the square for 'x2 + 12x - 1 = 0' gives:

(x+6)2−37=0

Hence solve the equation to find x.

x=±√37−6
x=6±√37
x=±√6−37
x=37±√6

0

/

1

Complete the square for the following quadratic equation.

x2−10x+16
(x-5)^2-9

[0/1]

Now, solve the equation:

(x−5)2−9=0
x=4 and x=2
x=1 and x=2
x=−4 and x=−2
x=8 and x=2

[0/1]

0

/

2

Complete the square for the following quadratic equation.

x2−6x+5
(x-3)^2-4

[0/1]

Now, solve the equation:

(x−3)2−4=0
x=5 and x=3
x=2 and x=1
x=5 and x=1
x=10 and x=−5

[0/1]

0

/

2