# SOLVE A QUADRATIC EQUATIONS USING SQUARE ROOTS

## About "Solve a quadratic equations using square roots"

Solve a quadratic equation using square roots :

Whenever we have a equation like x² = a, we can find the values of x by taking square root on both sides. Let us see some example problems based on the above concept.

Example 1 :

Solve for y

y² = 16

Solution :

To solve the equation y² = 16, we have to take square roots on both sides.

y² = 16

On the left side square and root will get canceled. Now on the right side, we will have 16. Since 16 is positive, we will have two real roots.

y = 16

y = √(4 x 4)  =  ± 4

Hence y = 4 and y = -4.

Example 2 :

Solve for x

x² + 8 = 20

Solution :

To solve the above equation, we have to isolate x², for that we have to subtract 8 on both sides.

x² + 8 - 8 = 28 - 8

x² = 20

Now we have to take square roots on both sides.

√x² = √20

x = √20

Now we have to split 20 as much as possible.

x = √(2 x 2 x 5)  =  ± 2√5

Hence x = 2√5 and x = -2√5

Example 3 :

Solve for x

2x² =  -72

Solution :

To solve the above equation, we have to isolate x², for that we have to divide by 2 on both sides.

2x²/2 =  -72/2

x² = -36

Now we have to take square roots on both sides.

√x² = √-36

x = √-36

Since the number inside the radical sign is negative, we will have two imaginary roots.

x = i√36

Now we have to split 36 as much as possible.

x = i√(2 x 2 x 3 x 3)  =  ± i (2 x 3)  =  ±6i

Hence x = 6i and x = -6i

Example 4 :

Solve for t

-5t² =  -500

Solution :

To solve the above equation, we have to isolate t², for that we have to divide by (-5) on both sides.

-5x²/(-5) =  -500/(-5)

x² = 100

Now we have to take square roots on both sides.

√x² = √100

x = √100

Since the number inside the radical sign is positive, we will have two real roots.

Now we have to split 100 as much as possible.

x = √(2 x 2 x 5 x 5)  =  ±  (2 x 5)  =  ± 10

Hence x = 10 and x = -10

Example 5 :

Solve for x

9x² + 10 =  91

Solution :

To solve the above equation, we have to isolate t², for that we have to subtract 10 on both sides.

9x² + 10 - 10 =  91 - 10

9x² = 81

Divide 9 on both sides

9x²/9 = 81/9

x²= 9

Now we have to take square roots on both sides.

√x² = √9

x = √9

Since the number inside the radical sign is positive, we will have two real roots.

Now we have to split 9 as much as possible.

x = √(3 x 3)  =  ±3

Hence x = 3 and x = -3

After having gone through the stuff given above, we hope that the students would have understood "Solve a quadratic equation using square roots".

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