What is the solution for 75 = -5t^2 + 40t

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation we have is a quadratic equation and will have two solutions.

75 = -5t^2 + 40t

=> 5t^2 - 40t + 75 = 0

=> t^2 - 8t + 15 = 0

=> t^2 - 5t - 3t + 15 = 0

=> t(t - 5) - 3(t - 5) = 0

=> (t - 3)(t - 5) = 0

=> t = 3 and t = 5

The solutions of 75 = -5t^2 + 40t are t = 3 and t = 5

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll use the symmetric property for the given expression and we'll get:

5t^2 - 40t = -75

We'll divide by 5 all over:

t^2 - 8t = -15

Now, we'll have to complete the square from the left side. For this purpose, we'll add both sides the number 16:

t^2 - 8t + 16 = 16 - 15

We'll recognize the square:

(t-4)^2 = 1

We'll consider 2 cases:

1) t - 4 = sqrt 1

t - 4 = 1 => t = 5

2) t - 4 = -sqrt 1

t - 4 = -1 => t = 3

There are 2 solutions for the equation above (since it's order is 2) and they are: {3 ; 5}.

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