t^2-20t+20=0

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Solution for t^2-20t+20=0 equation:


Simplifying
t2 + -20t + 20 = 0

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

Solving
20 + -20t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -20 + 100

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

Combine like terms: -20 + 100 = 80
100 + -20t + t2 = 80

Factor a perfect square on the left side:
(t + -10)(t + -10) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(t + -10) equal to 8.94427191 and -8.94427191.

Subproblem 1

t + -10 = 8.94427191 Simplifying t + -10 = 8.94427191 Reorder the terms: -10 + t = 8.94427191 Solving -10 + t = 8.94427191 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 = 8.94427191 + 10 Combine like terms: -10 + 10 = 0 0 + t = 8.94427191 + 10 t = 8.94427191 + 10 Combine like terms: 8.94427191 + 10 = 18.94427191 t = 18.94427191 Simplifying t = 18.94427191

Subproblem 2

t + -10 = -8.94427191 Simplifying t + -10 = -8.94427191 Reorder the terms: -10 + t = -8.94427191 Solving -10 + t = -8.94427191 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 = -8.94427191 + 10 Combine like terms: -10 + 10 = 0 0 + t = -8.94427191 + 10 t = -8.94427191 + 10 Combine like terms: -8.94427191 + 10 = 1.05572809 t = 1.05572809 Simplifying t = 1.05572809

Solution

The solution to the problem is based on the solutions from the subproblems. t = {18.94427191, 1.05572809}

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