Question

what is t in the quadratic equation $-5t^2 + 10t + 5 = 0$? use the keypad to enter the answer in the box. write your answer in 2 decimal places. $t_1 = square$ and $t_2 = square$

Explanation:

Step1: Identify quadratic coefficients

For $-5t^2 + 10t + 5 = 0$, we have $a=-5$, $b=10$, $c=5$.

Step2: Apply quadratic formula

Quadratic formula: $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:
$$t = \frac{-10 \pm \sqrt{10^2 - 4(-5)(5)}}{2(-5)}$$

Step3: Calculate discriminant

Compute $\sqrt{100 + 100} = \sqrt{200} = 10\sqrt{2} \approx 14.1421$

Step4: Solve for two roots

First root:
$$t_1 = \frac{-10 + 14.1421}{-10} = \frac{4.1421}{-10} \approx -0.41$$
Second root:
$$t_2 = \frac{-10 - 14.1421}{-10} = \frac{-24.1421}{-10} \approx 2.41$$

Answer:

$t_1 = -0.41$ and $t_2 = 2.41$