Answer:
x = [tex]\frac{1}{4}[/tex] ± [tex]\frac{1}{2}[/tex][tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2}[/tex] (4x - 1)² = 4 ( multiply both sides by 2 to clear the fraction )
(4x - 1)² = 8 ( take the square root of both sides )
4x - 1 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( add 1 to both sides )
4x = 1 ± 2[tex]\sqrt{2}[/tex] ( divide both sides by 4 )
x = [tex]\frac{1+/-2\sqrt{2} }{4}[/tex]
= [tex]\frac{1}{4}[/tex] ± [tex]\frac{1}{2}[/tex][tex]\sqrt{2}[/tex]
