Solve equation for t.

Question

h=-16t²+gt+b

 

answer must be in integers or fractions (two answers)

Answer 1

h=-16t^2+gt+b

-h=16t^2-gt-b

0=16t^2-gt-b+h

using the quadratic equation

a=16, b=-g, and c=-(b-h)

[g+√(g²+64(b-h))]/32=t

for some reason the + or - did not get printed correctly so there are 2 answers, g+√ etc and g-√ etc

Answer 2

We need to isolate the t terms.

 

 

Subtract b on both sides of the equation.

 

h - b = -16t² + gt

 

 

We have all t terms on one side of the equation.  Next, lets divide both sides of the equation by -16.  You will see why later on.

 

 

-(1/16)(h - b) = t² - (1/16)gt

 

-(1/16)h + (1/16)b = t² - (1/16)gt

 

 

 

Complete the square on the right side of the equation.  If we divide (1/16)g by 2, and square the result, and add both sides of the equation by that number, we will have a polynomial on the right side that we will be a perfect square.

 

-(1/16)h + (1/16)b + (1/1024)g² = t² - (1/16)gt + (1/1024)g²

 

(-1/16)h + (1/16)b + (1/1024)g² = (t - (1/32)g)(t - (1/32)g)

 

(-1/16)h + (1/16)b + (1/1024)g² = (t - (1/32)g)²

 

 

Square-root both sides of the equation.

 

±√[ (-1/16)h + (1/16)b + (1/1024)g² ] = t - 1/32

 

 

Add 1/32 on both sides of the equation.

 

(1/32) ± √[ (-1/16)h + (1/16)b + (1/1024)g² ] = t

 

 

The plus/minus sign indicates that we will have two answers.