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Quadratic Equation

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Hi guys can you please help me out with the solving of this quadratic equation asap .

Question :

Find the range of values of m such that for all x

m(x+1) is less than and equal to x^2.

(PS : if did not understand above, then check attachment).

thnx

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m(x+1)≤x2

x2-mx-m≥0

(x2-2×0.5m×x+(0.5m)2)-(0.5m)2-m≥0

(x-0.5m)2+(-m2/4-m)≥0

since (x-0.5m)2≥0 ∴(-m2/4-m)≥0 (For the eqn to be true for all value of x )

∴-m2-4m≥0

m2+4m≤0

m(m+4)≤0

-4≤m≤0

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