Solve the equation. Express radicals in simplest form

Question

A) (n-7)^2-25=0          B) (2r+3)^2=44

Answer 1

A)

 

(n - 7)² - 25 = 0

 

 

Add 25 on both sides of equation.

 

(n - 7)² = 25

 

 

Square-root both sides of equation to undo the exponent.

 

n - 7 = ±√25

 

 

Add 7 on both sides of equation.

 

n = 7 ± √25

n = 7 ± 5

 

n = 7 - 5               and              n = 7 + 5

 

n = 2                    and              n = 12

 

 

B)  We do the same procedure as A.

 

(2r - 3)² = 44

 

 

Square-root both sides of equation.

 

2r + 3 = ±√44

 

2r + 3 = ±√4√11

 

2r + 3 = ±2√11

 

 

Subtract 3 on both sides of equation.

 

2r = -3 ± 2√11

 

 

Divide both sides of equation by 2.

 

r = (-3 ± 2√11) / 2

 

r = (-3/2) ± √11

 

r = (-3/2) - √11                   and               r = (-3/2) + √11