Question

Anyone please i need help,
Solve the given quadratic equations by extracting square roots.​

Answer 1

see explanation

Explanation:

(1)

(x - 4)² = 49 ( take square root of both sides )

`√((x-4)^2)` = ±
`√(49)` [ note ± , that is plus or minus )

x - 4 = ± 7 ( add 4 to both sides )

x = 4 ± 7 , that is

x = 4 - 7 = - 3 or x = 4 + 7 = 11

(2)

2x² = 18 ( divide both sides by 2 )

x² = 9 ( take square root of both sides )

`√(x^2)` = ±
`√(9)` , that is

x = ± 3

(3)

y² = 121 ( take square root of both sides )

`√(y^2)` = ±
`√(121)` , that is

y = ± 11

(4)

4y² = 16 ( divide both sides by 4 )

y² = 4 ( take square root of both sides )

`√(y^2)` = ±
`√(4)` , that is

y = ± 4

(5)

2(x - 5)² = 32 ( divide both sides by 2 )

(x - 5)² = 16 ( take square root of both sides )

`√((x-5)^2)` = ±
`√(16)` , that is

x - 5 = ± 4 ( add 5 to both sides )

x = 5 ± 4

Then

x = 5 - 4 = 1 or x = 5 + 4 = 9