Solve Using the Quadratic Formula 1.3=(4.2)t+0.5(-9.8)t^2

Problem

1.3=4.2*t+0.5*(−9.8)*t2

Solution

1. Simplify the equation by performing the multiplication on the right side.

0.5*(−9.8)=−4.9

1.3=4.2*t−4.9*t2

2. Rearrange the equation into standard quadratic form a*t2+b*t+c=0 by moving all terms to one side.

4.9*t2−4.2*t+1.3=0

3. Identify the coefficients a b and c for use in the quadratic formula.

a=4.9

b=−4.2

c=1.3

4. Apply the quadratic formula t=(−b±√(,b2−4*a*c))/(2*a)

t=(−(−4.2)±√(,(−4.2)2−4*(4.9)*(1.3)))/(2*(4.9))

5. Calculate the discriminant b2−4*a*c to determine the nature of the roots.

(−4.2)2−4*(4.9)*(1.3)=17.64−25.48

17.64−25.48=−7.84

6. Conclude that since the discriminant is negative, there are no real solutions. The solutions involve the imaginary unit i=√(,−1)

t=(4.2±√(,−7.84))/9.8

t=(4.2±2.8*i)/9.8

7. Simplify the fractions to find the final complex values for t

t=4.2/9.8±2.8/9.8*i

t=3/7±2/7*i

Final Answer

t=(3±2*i)/7

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