1. mr-mathematics.com Recapping: Algebraic notation and square numbers.
x and y are both integers and greater than zero.
Find the values of x and y.
ANS
mr-mathematics.com

2. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x + 8 = 0
b) x2 + 2x - 4 = 0
c) x2 + 8x + 5 = 0
d) x2 – 2x – 3 = 0
e) x2 - x - 2 = 0
f) x2 – 5x – 4 = 0
ANS
ANS
ANS
ANS
ANS
ANS
mr-mathematics.com

3. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
g) x2 + 3 = 5x h) x2 = 5 - 9x
ANS
ANS
ANS
ANS
ANS
ANS
ANS
ANS
mr-mathematics.com

4. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
The area of the shape is 20 cm².
ANS
a) Set up an equation in terms of x.
b) Solve the equation to find the value of x.
Leave your answer in simplified surd form.
mr-mathematics.com

5. mr-mathematics.com Recapping: Algebraic notation and square numbers.
x and y are both integers and greater than zero.
Find the values of x and y.
x = 7, y = 2
Go Back
mr-mathematics.com

6. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x + 8 = 0, x = -4, x = -2
b) x2 + 2x - 4 = 0
c) x2 + 8x + 5 = 0
d) x2 – 2x – 3 = 0
e) x2 - x - 2 = 0
f) x2 – 5x – 4 = 0
Go Back
mr-mathematics.com

7. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x + 8 = 0, x = -4, x = -2
b) x2 + 2x - 4 = 0, 𝑥=−1±√5
c) x2 + 8x + 5 = 0
d) x2 – 2x – 3 = 0
e) x2 - x - 2 = 0
f) x2 – 5x – 4 = 0
Go Back
mr-mathematics.com

8. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x + 8 = 0, x = -4, x = -2
b) x2 + 2x - 4 = 0, 𝑥=−1±√5
c) x2 + 8x + 5 = 0, 𝑥=−4±√11
d) x2 – 2x – 3 = 0
e) x2 - x - 2 = 0
f) x2 – 5x – 4 = 0
Go Back
mr-mathematics.com

9. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x + 8 = 0, x = -4, x = -2
b) x2 + 2x - 4 = 0, 𝑥=−1±√5
c) x2 + 8x + 5 = 0, 𝑥=−4±√11
d) x2 – 2x – 3 = 0, x = -1, x = 3
e) x2 - x - 2 = 0
f) x2 – 5x – 4 = 0
Go Back
mr-mathematics.com

10. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x + 8 = 0, x = -4, x = -2
b) x2 + 2x - 4 = 0, 𝑥=−1±√5
c) x2 + 8x + 5 = 0, 𝑥=−4±√11
d) x2 – 2x – 3 = 0, x = -1, x = 3
e) x2 - x - 2 = 0, x = -1, x = 2
f) x2 – 5x – 4 = 0
Go Back
mr-mathematics.com

11. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x + 8 = 0, x = -4, x = -2
b) x2 + 2x - 4 = 0, 𝑥=−1±√5
c) x2 + 8x + 5 = 0, 𝑥=−4±√11
d) x2 – 2x – 3 = 0, x = -1, x = 3
e) x2 - x - 2 = 0, x = -1, x = 2
f) x2 – 5x – 4 = 0, 𝑥= 5 ± √41 2
Go Back
mr-mathematics.com

12. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
g) x2 + 3 = 5x h) x2 = 5 - 9x
Go Back
mr-mathematics.com

13. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13 𝑥=−4±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
g) x2 + 3 = 5x h) x2 = 5 - 9x
Go Back
mr-mathematics.com

14. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13 𝑥=−4±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
𝑥=5±√19
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
g) x2 + 3 = 5x h) x2 = 5 - 9x
Go Back
mr-mathematics.com

15. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13 𝑥=−4±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
𝑥=5±√19 𝑥=6±√34
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
g) x2 + 3 = 5x h) x2 = 5 - 9x
Go Back
mr-mathematics.com

16. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13 𝑥=−4±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
𝑥=5±√19 𝑥=6±√34
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
𝑥=3±2√2
g) x2 + 3 = 5x h) x2 = 5 - 9x
Go Back
mr-mathematics.com

17. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13 𝑥=−4±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
𝑥=5±√19 𝑥=6±√34
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
𝑥=3±2√2 𝑥=−1±√3
g) x2 + 3 = 5x h) x2 = 5 - 9x
Go Back
mr-mathematics.com

18. 𝑥= 5 ± √13 2 mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13 𝑥=−4±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
𝑥=5±√19 𝑥=6±√34
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
𝑥=3±2√2 𝑥=−1±√3
g) x2 + 3 = 5x h) x2 = 5 - 9x
𝑥= 5 ± √13 2
Go Back
mr-mathematics.com

19. 𝑥= 5 ± √13 2 𝑥= −9 ± √101 2 mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
Solve these equations by completing the square:
a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0
𝑥=−3±√13 𝑥=−4±√13
c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0
𝑥=5±√19 𝑥=6±√34
e) x2 – 6x + 1 = 0 f) x2 + 2x = 2
𝑥=3±2√2 𝑥=−1±√3
g) x2 + 3 = 5x h) x2 = 5 - 9x
𝑥= 5 ± √ 𝑥= −9 ± √101 2
Go Back
mr-mathematics.com

20. mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square.
The area of the shape is 20 cm².
a) Set up an equation in terms of x. x2 + 5x – 18 = 0
b) Solve the equation to find the value of x.
Leave your answer in simplified surd form.
𝑥= −5±√97 2
Go Back
mr-mathematics.com