x - the number
[tex]x^2+5x=176 \\
x^2+5x-176=0 \\ \\
a=1 \\ b=5 \\ c=-176 \\
b^2-4ac=5^2-4 \times 1 \times (-176)=25+704=729 \\ \\
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-5 \pm \sqrt{729}}{2 \times 1}=\frac{-5 \pm 27}{2} \\
x=\frac{-5 - 27}{2} \ \lor \ x=\frac{-5 +27}{2} \\
x=\frac{-32}{2} \ \lor \ x=\frac{22}{2} \\
x=-16 \ \lor \ x=11[/tex]
The number is -16 or 11.
