Final answer:
To solve the equation 5t² - 35.16t - 114 = 0, use the quadratic formula. The solutions are t = 3.96 and t = -1.03.
Step-by-step explanation:
To solve the equation 5t² - 35.16t - 114 = 0, we can use the quadratic formula. The quadratic formula is given by t = (-b ± √(b² - 4ac))/(2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. In this case, a = 5, b = -35.16, and c = -114. Substituting these values into the quadratic formula, we get t = (35.16 ± √((-35.16)² - 4*5*(-114)))/(2*5).
Simplifying this expression, we have t = (35.16 ± √(1238.6656 + 2280))/10.
Continuing the simplification, we get t = (35.16 ± √3518.6656)/10.
Calculating the square root and dividing by 10, we have two solutions: t = 3.96 and t = -1.03.