Everything Maths Grade 11

7.3 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS

5. Write the left hand side as a perfect square: (x + 1)^2 − 4 = 0


6. You should then be able to factorise the equation in terms of difference of squares and then solve
   for x:

[(x + 1)− 2][(x + 1) + 2)] = 0

(x− 1)(x + 3) = 0

∴ x = 1 or x =− 3

Example 4: Solving Quadratic Equations by Completing the Square

QUESTION

Solve by completing thesquare:

x^2 − 10 x− 11 = 0

SOLUTION

Step 1 : Write the equation in the form ax^2 + bx + c = 0

x^2 − 10 x− 11 = 0

Step 2 : Take the constant overto the right hand side of the equation

x^2 − 10 x = 11

Step 3 : Check that the coefficient of the x^2 term is 1.

The coefficient of the x^2 term is 1.

Step 4 : Take half the coefficient of the x term, square it and addit to both sides

The coefficient of the x term is− 10. Therefore, half of thecoefficient of the x

term will be(− 2 10)=− 5 and the square of it will be (−5)^2 = 25. Therefore:

x^2 − 10 x + 25 = 11 + 25

Step 5 : Write the left hand side as a perfect square

(x− 5)^2 − 36 = 0

Step 6 : Factorise equation as difference of squares

(x− 5)^2 − 36 = 0

[(x− 5) + 6][(x− 5)− 6] = 0

Step 7 : Solve for the unknownvalue