Answer:
x = - [tex]\frac{1}{2}[/tex], x = 3
Step-by-step explanation:
Given
(4x - 5)² = 49 ( take the square root of both sides )
4x - 5 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 5 to both sides )
4x = 5 ± 7, thus
4x = 5 - 7 = - 2 ( divide both sides by 4 )
x = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
or
4x = 5 + 7 = 12 ( divide both sides by 4 )
x = 3
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = - [tex]\frac{1}{2}[/tex]
left side = (- 2 - 5)² = (- 7)² = 49 = right side ⇒ solution
x = 3
left side = (12 - 5)² = 7² = 49 = right side ⇒ solution
