**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**

*x*^{2}- 14*x*+ 20 = -4 by finding perfect squares.**Solution:**

**Step 1:**

**Given quadratic equation is**

*x*^{2}- 14*x*+ 20 = -4.**Rewrite the equation so that it contains only x term on left side**

**x**

^{2}– 14x = -20 – 4**x**

^{2}– 14x = - 24**Step 2:**

**Dividing 14 by 2 we have 7. Take a square for 7 which is 49.**

**Add 49 on sides**

**x**

^{2}– 14x + 49 = -24 + 49**x**

^{2}– 14x + 49 = 25**Step 3:**

**(x – a)**

^{2}= x^{2}– 2ax + a^{2}**x**

^{2}– 2(x)(7) + 7^{2}= 25**(x – 7)**

^{2}= 25**(x – 7)**

^{2}= 5^{2}**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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