Some quadratic equations can be solved by bringing it into perfect squares, and then taking square root on both sides.
Look at the following example.
Example:
Solve the quadratic equation x2 - 14x + 20 = -4 by finding perfect squares.
Solution:
Step 1:
Given quadratic equation is x2 - 14x + 20 = -4.
Rewrite the equation so that it contains only x term on left side
x2 – 14x = -20 – 4
x2 – 14x = - 24
Step 2:
Dividing 14 by 2 we have 7. Take a square for 7 which is 49.
Add 49 on sides
x2 – 14x + 49 = -24 + 49
x2 – 14x + 49 = 25
Step 3:
(x – a)2 = x2 – 2ax + a2
x2 – 2(x)(7) + 72 = 25
(x – 7)2 = 25
(x – 7)2 = 52
Step 4:
Take square root on both sides.
x – 7 = 5 or x – 7 = -5
Step 5:
x – 7 = 5 x – 7 = -5
x = 12 x = 2
Step 6:
So, the solution set is {2, 12}.
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