Question

1. $t^2 - 26t = 56$

Explanation:

Step1: Rearrange to standard quadratic form

$t^2 - 26t - 56 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=1$, $b=-26$, $c=-56$.
$t=\frac{26\pm\sqrt{(-26)^2-4(1)(-56)}}{2(1)}$

Step3: Calculate discriminant

$\sqrt{676 + 224}=\sqrt{900}=30$

Step4: Solve for t values

$t=\frac{26+30}{2}$ and $t=\frac{26-30}{2}$

Answer:

$t=28$ and $t=-2$