# Solve nonlinear equation

Please help me to solve the following nonlinear equation, such that I used ''FindRoot" but no result

the equation is -10.499999997354678 (-0.006630671819814823+ x^3 +x^2(1.1599999999940591- 0.7999999999851477 Sqrt[1 + x]))-(-0.7(-0.1233952365163843+x) + 3.4999999989155866 (-0.13078703184428012 + x Sqrt[1 + x])) == 0

You could try NSolve instead. In Version 12.2 it gives

ClearAll[x];
eq = -10.499999997354678 (-0.006630671819814823 + x^3 +
x^2 (1.1599999999940591 -
0.7999999999851477 Sqrt[
1 + x])) - (-0.7 (-0.1233952365163843 + x) +
3.4999999989155866 (-0.13078703184428012 + x Sqrt[1 + x])) == 0;
NSolve[eq, x]


This solution

{{x -> -0.962771}, {x -> -0.510822 - 0.680662 I}, {x -> -0.510822 +
0.680662 I}, {x -> 0.123395}}


If you want in Reals, you could do

NSolve[eq, x, Reals]


which gives

{{x -> -0.962771}, {x -> 0.123395}}

\$Version

(* "12.2.0 for Mac OS X x86 (64-bit) (December 12, 2020)" *)

Clear["Global*"]

f[x_] = -10.499999997354678 (-0.006630671819814823 + x^3 +
x^2 (1.1599999999940591 -
0.7999999999851477 Sqrt[
1 + x])) - (-0.7 (-0.1233952365163843 + x) +
3.4999999989155866 (-0.13078703184428012 + x Sqrt[1 + x]));

FunctionDomain[f[x], x]

(* x >= -1 *)

Plot[f[x], {x, -1, 1}]


NSolve[{f[x] == 0, -1 < x < 1}, x]

(* {{x -> -0.962771}, {x -> 0.123395}} *)

Solve[{f[x] == 0, -1 < x < 1}, x] // Quiet

(* {{x -> -0.962771}, {x -> 0.123395}} *)

FindRoot[f[x] == 0, {x, #}] & /@ {-1, .5}

(* {{x -> -0.962771}, {x -> 0.123395}} *)

• Thank you so much dears. Thanks for all your Help Jan 24, 2021 at 6:07