Let the number be x
Then square x means
[tex]x^2[/tex]Now we need to subtract 45 from it, then
[tex]x^2-45[/tex]The result means equating it by 4 times the number, which means 4 times x
[tex]\begin{gathered} x^2-45=4\times x \\ \\ x^2-45=4x \end{gathered}[/tex]Subtract 4x from each side
[tex]\begin{gathered} x^2-4x-45=4x-4x \\ \\ x^2-4x-45=0 \end{gathered}[/tex]We will factor the left side
[tex]\begin{gathered} x^2=(x)(x) \\ \\ -45=(5)(-9) \\ \\ (x)(5)+(x)(-9)=5x-9x=-4x \\ \\ x^2-4x-45=(x+5)(x-9) \end{gathered}[/tex]Then the equation is
[tex](x+5)(x-9)=0[/tex]Equate each factor by 0
[tex]\begin{gathered} x+5=0 \\ \\ x+5-5=0-5 \\ \\ x=-5 \end{gathered}[/tex]The negative solution is -5
The number is -5
