Question

Solve the following quadratic equation by extracting square roots.
1.) r²-100=0
2.) 4x²-225=0
3.) 3h²-147=0
4.) ( x-4 )1=169
5.) ( k+7 )²=289
6.) (2s-1)²=225

Answer 1

-r2-100 = 0

Add 100 to both sides of the equation :

-r2 = 100

Multiply both sides of the equation by (-1) : r2 = -100

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

r = ± √ -100

In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1

Accordingly, √ -100 =

√ -1• 100 =

√ -1 •√ 100 =

i • √ 100

Can √ 100 be simplified ?

Yes! The prime factorization of 100 is

2•2•5•5

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 100 = √ 2•2•5•5 =2•5•√ 1 =

± 10 • √ 1 =

± 10

The equation has no real solutions. It has 2 imaginary, or complex solutions.

r= 0.0000 +10.0000 i

r= 0.0000 -10.0000 i

२) picture

३) picture

४) picture

५) Simplifying

(k + 7) * 2 = 289

Reorder the terms:

(7 + k) * 2 = 289

Reorder the terms for easier multiplication:

2(7 + k) = 289

(7 * 2 + k * 2) = 289

(14 + 2k) = 289

Solving

14 + 2k = 289

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-14' to each side of the equation.

14 + -14 + 2k = 289 + -14

Combine like terms: 14 + -14 = 0

0 + 2k = 289 + -14

2k = 289 + -14

Combine like terms: 289 + -14 = 275

2k = 275

Divide each side by '2'.

k = 137.5

Simplifying

k = 137.5

६)(2s-1)^2 = 225 = (15)^2. Taking sqrt of both (2s-1)^2 and (15)^2 gives 2s-1 = (+/-)15. Then s = (1/2)[1(+/-)15] = (1/2)[-14 or 16] = -7 or 8.

Answer 2

Given : 1.) r²-100=0

2.) 4x²-225=0

3.) 3h²-147=0

4.) ( x-4 )1=169

5.) ( k+7 )²=289

6.) (2s-1)²=225

To Find :  extracting square roots.

Solution:

r²-100=0

=>  r² = 100

=> r = ± 10

4x²-225=0

=> x² = 225/4

=> x = ± 15/2

3h²-147=0

=> 3h² = 147

=> h² = 49

=> h = ± 7

( x-4 )²=169

=> x - 4 = ±13

=> x = 4 ± 13

=> x = 17 , - 9

( k+7 )²=289

=> k +  7 = ± 17

=> k = - 7 ± 17

=> k = -24 , 10

(2s-1)²=225

=> 2s - 1 = ± 15

=> 2s =   1  ± 15

=> 2s = -14 , 16

=> s = - 7 , 8

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