Question

Solve (2x + 5)² – 7 = 0 using extracting the square root.​

Answer 1

Answer: x =
`( √(7)-5)/(2)`

x =
`( -√(7)-5)/(2)`

Step-by-step explanation:

`(2x + 5)^(2) - 7 = 0`

Add 7 to both sides of the equation.

`(2x + 5)^(2) - 7 + 7= 0 + 7`

Subtracting 7 from itself leaves 0.

`(2x + 5)x^(2) =7`

Take the square root of both sides of the equation.

`2x + 5 = √(7) \\2x + 5 = -√(7)`

Subtract 5 from both sides of the equation.

`2x + 5 - 5 = √(7) - 5 \\2x + 5 - 5 = - √(7) - 5`

Subtracting 5 from itself leaves 0.

`2x = √(7) - 5 \\2x = - √(7) - 5`

Subtract 5 from
`√(7)`.

`2x = √(7) - 5`

Subtract 5 from
`-√(7)`.

`2x = -√(7) - 5`

Divide both sides by 2.

`(2x)/(2) =( √(7)-5)/(2) \\(2x)/(2) =(- √(7)-5)/(2)`

Dividing by 2 undoes the multiplication by 2.

`x=( √(7)-5)/(2)\\x=( -√(7)-5)/(2)`