1. Solving Quadratic Equations by the Quadratic Formula

2. Method of taking square roots
In fact, for quadratic equations in the form (x + m)2 = n, we can solve them by taking square roots.
We have learnt how to solve quadratic equations ax2 + bx + c = 0 by the factor method.
e.g. (x – 3)2 = 16

3. Follow-up question How to solve (x + 5)2 = –9? (x + 5)2 = –9
∴ The equation has no real roots.
is not a real number.
Follow-up question
Solve (x + 1)2 = 25 by taking square roots.
(x + 1)2 = 25

4. Yes. There is a formula which can solve all quadratic equations.
x2 + 3x – 2 cannot be factorized by cross-method. Is there any way to solve x2 + 3x – 2 = 0?
Yes. There is a formula which can solve all quadratic equations.

5. Rewrite the equation in the form (x + m)2 = n.
ax2 + bx + c = 0
, where a  0
Step 1
Rewrite the equation in the form (x + m)2 = n.
Divide both sides by a.
Add the term
to both
sides. 2 ç è æ a b

6. Step 2
Take square roots on both sides.
Step 3
Express the roots in terms of a, b and c.
Quadratic formula

7. Using the quadratic formula
Now, I can solve x2 + 3x – 2 = 0.
a = 1
c = –2 ∴
b = 3

8. Solve 2x2  4x + 3 = 0 using the quadratic formula.
Follow-up question
Solve 2x2  4x + 3 = 0 using the quadratic formula.
 Substitute a = 2, b = –4 and c = 3 into the formula.
∵ is not a real number.
∴ The equation has no real roots.