20t-t^2=50

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Solution for 20t-t^2=50 equation:


Simplifying
20t + -1t2 = 50

Solving
20t + -1t2 = 50

Solving for variable 't'.

Reorder the terms:
-50 + 20t + -1t2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 20t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
50 + -20t + t2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -20t + -50 + t2 = 0 + -50

Reorder the terms:
50 + -50 + -20t + t2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -20t + t2 = 0 + -50
-20t + t2 = 0 + -50

Combine like terms: 0 + -50 = -50
-20t + t2 = -50

The t term is -20t.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20t + 100 + t2 = -50 + 100

Reorder the terms:
100 + -20t + t2 = -50 + 100

Combine like terms: -50 + 100 = 50
100 + -20t + t2 = 50

Factor a perfect square on the left side:
(t + -10)(t + -10) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(t + -10) equal to 7.071067812 and -7.071067812.

Subproblem 1

t + -10 = 7.071067812 Simplifying t + -10 = 7.071067812 Reorder the terms: -10 + t = 7.071067812 Solving -10 + t = 7.071067812 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + t = 7.071067812 + 10 t = 7.071067812 + 10 Combine like terms: 7.071067812 + 10 = 17.071067812 t = 17.071067812 Simplifying t = 17.071067812

Subproblem 2

t + -10 = -7.071067812 Simplifying t + -10 = -7.071067812 Reorder the terms: -10 + t = -7.071067812 Solving -10 + t = -7.071067812 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + t = -7.071067812 + 10 t = -7.071067812 + 10 Combine like terms: -7.071067812 + 10 = 2.928932188 t = 2.928932188 Simplifying t = 2.928932188

Solution

The solution to the problem is based on the solutions from the subproblems. t = {17.071067812, 2.928932188}

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