Answer:
x ≈ 1.5004
Step-by-step explanation:
We suppose your equation is ...
[tex]x^3+x-7=-3\sqrt{x-1}[/tex]
Squaring both sides and subtracting the right side gives ...
[tex]x^6 +2x^4 -14x^3 +x^2 -23x +58 = 0[/tex]
This 6th-degree equation has two positive real roots, near x=1.5, and x=2. The root at x=2 is extraneous. The one near x=1.5 is irrational.
