QUADRATIC EQUATION IN THE FORM X SQUARE EQUAL TO K

Solve for x :

Example 1 :

x²  =  16

Solution :

x²  =  16

By taking square roots on both sides, we get

x  =  √16

x  =  ± 4

So, the value of x is ± 4

Example 2 :

12x²  =  72

Solution :

12x²  =  72

Dividing by 12 on both sides, we get

x²  =  72/12

x²  =  6

By taking square roots

x  =  ± √6

So, the value of x is ± √6

Example 3 :

2x² + 1  =  19

Solution :

2x² + 1  =  19

Subtracting 1 on both sides,

2x²  =  18

Dividing by 2 on both sides.

x²  =  9

x  =  √9

x  =  ± 3

So, the value of x is ± 3

Example 4 :

2x² + 7  =  13

Solution :

2x² + 7  =  13

Subtract by 7 on both sides, we get

2x²  =  6

x²  =  3

x  =  ± √3

So, the value of x is ± √3

Example 5 :

3x²  =  - 12

Solution :

3x²  =  - 12

x²  =  - 12/3

x²  =  - 4

x  =  √-4

There is no real solution.

Example 6 :

1 – 3x²  =  10

Solution :

1 - 3x²  =  10

1 - 3x²  =  10

- 3x²  =  10 - 1

- 3x²  =  9

x²  =  - 9/3

x²  =  - 3

x  =  √-3

It has no solution.

Solve for x :

Example 7 :

(x – 2)²  =  9

Solution :

(x – 2)²  =  9

Taking the square root on both sides,

√(x – 2)²  =  √9

x – 2  =  ±3

So, the value of x is 5 or - 1.

Example 8 :

(x + 4)²  =  25

Solution :

(x + 4)²  =  25

Taking the square root on both sides,

√(x + 4)²  =  √25

x + 4  =  ±5

So, the value of x is 1 or - 9

Example 9 :

(x + 3)²  =  - 1

Solution :

(x + 3)²  =  - 1

Taking the square root on both sides,

(x + 3)  =  √- 1

So, there is no real solution.

Example 10 :

(x - 4)²  =  2

Solution :

(x - 4)²  =  2

Taking the square root on both sides,

√(x - 4)²  =  √2

x - 4  =  ± √2

x  =  4 ± √2

So, the value of x is 4 ± √2

Example 11 :

(x + 3)²  =  - 7

Solution :

(x + 3)²  =  - 7

Taking the square root on both sides,

√(x + 3)²  =  √- 7

x + 3  =  √-7

So, there is no real solution.

Example 12 :

(x + 2)²  =  0

Solution :

(x + 2)²  =  0

Taking the square root on both sides,

√(x + 2)²  =  √0

x + 2  =  0

x  =  - 2

So, the value of x is - 2

Example 13 :

(2x + 5)²  =  0

Solution :

(2x + 5)²  =  0

Taking the square root on both sides,

√(2x + 5)²  =  √0

2x + 5  =  0

2x  =  - 5

x  =  - 5/2

x  =  - 2  1/2

So, the value of x is – 2 1/2

Example 14 :

(3x - 2)²  =  4

Solution :

(3x - 2)²  =  4

Taking the square root on both sides,

√(3x - 2)²  =  √4

3x - 2  =  ± 2

So, the value of x is 4/3 or 0

Example 15 :

1/3 (2x - 1)²  =  8

Solution :

1/3 (2x - 1)²  =  8

(2x – 1)²  =  24

Taking the square root on both sides,

√(2x - 1)²  =  √24

2x - 1  =  ± √24

2x  =  ± √24 + 1

x  =  ±(√24 + 1)/2

x  =  (1 ± 2√6)/2

So, the value of x is (1 ± 2√6)/2.

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