1t^2-300t+600=0

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Solution for 1t^2-300t+600=0 equation:


Simplifying
1t2 + -300t + 600 = 0

Reorder the terms:
600 + -300t + 1t2 = 0

Solving
600 + -300t + 1t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -300t + -600 + t2 = 0 + -600

Reorder the terms:
600 + -600 + -300t + t2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -300t + t2 = 0 + -600
-300t + t2 = 0 + -600

Combine like terms: 0 + -600 = -600
-300t + t2 = -600

The t term is -300t.  Take half its coefficient (-150).
Square it (22500) and add it to both sides.

Add '22500' to each side of the equation.
-300t + 22500 + t2 = -600 + 22500

Reorder the terms:
22500 + -300t + t2 = -600 + 22500

Combine like terms: -600 + 22500 = 21900
22500 + -300t + t2 = 21900

Factor a perfect square on the left side:
(t + -150)(t + -150) = 21900

Calculate the square root of the right side: 147.986485869

Break this problem into two subproblems by setting 
(t + -150) equal to 147.986485869 and -147.986485869.

Subproblem 1

t + -150 = 147.986485869 Simplifying t + -150 = 147.986485869 Reorder the terms: -150 + t = 147.986485869 Solving -150 + t = 147.986485869 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + t = 147.986485869 + 150 Combine like terms: -150 + 150 = 0 0 + t = 147.986485869 + 150 t = 147.986485869 + 150 Combine like terms: 147.986485869 + 150 = 297.986485869 t = 297.986485869 Simplifying t = 297.986485869

Subproblem 2

t + -150 = -147.986485869 Simplifying t + -150 = -147.986485869 Reorder the terms: -150 + t = -147.986485869 Solving -150 + t = -147.986485869 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + t = -147.986485869 + 150 Combine like terms: -150 + 150 = 0 0 + t = -147.986485869 + 150 t = -147.986485869 + 150 Combine like terms: -147.986485869 + 150 = 2.013514131 t = 2.013514131 Simplifying t = 2.013514131

Solution

The solution to the problem is based on the solutions from the subproblems. t = {297.986485869, 2.013514131}

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