[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1. }[/tex]
[tex]\mathsf{5x^2 - 6x - 2 = 0}[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve:}[/tex]
[tex]\mathsf{x = \dfrac{-(-6)\pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathsf{x = \dfrac{6 \pm \sqrt{76}}{10}}[/tex]
[tex]\huge\textbf{Simplify that as well:}[/tex]
[tex]\mathsf{x = \dfrac{3}{5} + \dfrac{1}{5}\sqrt{19}\ or\ x = \dfrac{3}{5} + (-\dfrac{1}{5})\sqrt{19}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x \approx 1.5 \ or\ x\approx -0.3{}\ }}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{x^2 + 3x = 40}[/tex]
[tex]\huge\textbf{Subtract 40 to both sides:}[/tex]
[tex]\mathsf{x^2 + 3x - 40 = 40 - 40}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x^2+ 3x - 40 = 0}[/tex]
[tex]\huge\textbf{Factor the left side of the equation:}[/tex]
[tex]\mathsf{(x - 5)\times (x + 8) = 0}[/tex]
[tex]\mathsf{(x - 5)(x + 8) = 0}[/tex]
[tex]\huge\textbf{Set the factors to equal to 0:}[/tex]
[tex]\mathsf{x - 5 = 0 \ or\ even\ x + 8 = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = 5\ or\ x = -8}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 5\ or \ x = -8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
