Everything Maths Grade 11

7.4 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS

Leave the left hand sidewritten as a perfect square

(x− 2)^2 = 12

Step 9 : Take the square root on both sides of the equation

x− 2 =±

√

12

Step 10 : Solve for x

Therefore x = 2−

√

12 or x = 2 +

√

12

Compare to answer in step 7.

See video: VMeyf at http://www.everythingmaths.co.za

Exercise 7 - 2

Solve the following equations by completing thesquare:

1. x^2 + 10x− 2 = 0


2. x^2 + 4x + 3 = 0


3. x^2 + 8x− 5 = 0


4. 2 x^2 + 12x + 4 = 0


5. x^2 + 5x + 9 = 0


6. x^2 + 16x + 10 = 0


7. 3 x^2 + 6x− 2 = 0


8. z^2 + 8z− 6 = 0


9. 2 z^2 − 11 z = 0


10. 5 + 4z− z^2 = 0

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 018q (2.) 018r (3.) 018s (4.) 018t (5.) 018u (6.) 018v

(7.) 018w (8.) 018x (9.) 018y (10.) 018z

7.4 Solution by the Quadratic Formula

EMBAI

It is not always possibleto solve a quadratic equation by factorising andsometimes it is lengthyand

tedious to solve a quadratic equation by completing the square. In these situations, you can use the

quadratic formula that gives the solutionsto any quadratic equation.