Step 1
Write the equation.
[tex]t^2\text{ + 1t - 30 = 0}[/tex]Step 2:
Write the quadratic equation formula.
[tex]\begin{gathered} ^{} \\ To\text{ solve for t} \\ \text{From at}^2\text{ + bt + c = 0} \\ t\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]Step 3:
Write the values of a , b and c from the given quadratic equation.
[tex]\begin{gathered} \text{a = 1 , b = 1, c = -30} \\ t\text{ = }\frac{-1\pm\sqrt[]{1^2-\text{ 4}\times(1)\times(-30)}}{2\times1} \\ t\text{ = }\frac{-1\pm\sqrt[]{1^{}+\text{ 120}}}{2} \\ t\text{ = }\frac{-1\pm\sqrt[]{\text{12}1}}{2} \end{gathered}[/tex]Step 4:
A)
[tex]\begin{gathered} \text{Next, compare} \\ t\text{ = }\frac{-1\pm\sqrt[]{\text{12}1}}{2}\text{ with }t\text{ = }\frac{N\pm\sqrt[]{D}}{M} \\ N\text{ = -1} \\ D\text{ = 121} \\ \text{M = 2} \end{gathered}[/tex]B)
Solve for the values of t
[tex]\begin{gathered} t\text{ = }\frac{-1\pm\sqrt[]{\text{12}1}}{2} \\ \text{t = }\frac{-1\pm11}{2} \\ \text{t = }\frac{-1+11}{2}\text{ , t = }\frac{-1\text{ - 11}}{2} \\ \text{t = }\frac{10}{2}\text{ , t = }\frac{-12}{2} \\ \text{t = 5 , -6} \end{gathered}[/tex]The solutions to the quadratic equation are:
t = 5 , -6
