4 х^2 + 4x-18|2x+1| + 46=0

4 х² + 4x-18|2x+1| + 46=0

4x²+4x-18 (2x+1) + 46=0

4x²+4x-36x-18+46=0

4x²-32x+28=0

x²-8x+7=0

x²-x-7x+7=0

x (x-1) - 7 (x-1) = 0

(x-7) (x-1) = 0

x=7 ∨ x=1

или

4x²+4x-18 (-2x-1) + 46=0

4x²+4x+36x+18+46=0

4x²+40x+64=0

x²+10x+16=0

x²+2x+8x+16=0

x (x+2) + 8 (x+2) = 0

(x+8) (x+2) = 0

x=-8 ∨ x=-2

x=-8 ∨ x=-2 ∨ x=1 ∨ x=7

4 х^2 + 4x-18|2x+1| + 46=0

a) 2x+1>0 = >x>-1/2

4x^2+4x-18 * (2x+1) + 46=0

4x^2+4x-36x-18+46=0

4x^2-32x+28=0

x^2-8x+7=0

D=36

x=1

x=7

б) x<-1/2

4x^2+4x+18 (2x+1) + 46=0

4x^2+4x+36x+18+46=0

4x^2+40x+64=0

x^2+10x+16=0

D=36

x=-2

x=-8

ответ: x=1; x=7; x=-2; x=-8