Question

what is perfect square method

Answer 1

Answer:

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}.

You may try the questions from factoring method and check your answer using quadratic solver.