300t-5*t*t=1

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Solution for 300t-5*t*t=1 equation:


Simplifying
300t + -5t * t = 1

Multiply t * t
300t + -5t2 = 1

Solving
300t + -5t2 = 1

Solving for variable 't'.

Reorder the terms:
-1 + 300t + -5t2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 300t + -5t2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.2 + -60t + t2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -60t + -0.2 + t2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -60t + t2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -60t + t2 = 0 + -0.2
-60t + t2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-60t + t2 = -0.2

The t term is -60t.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60t + 900 + t2 = -0.2 + 900

Reorder the terms:
900 + -60t + t2 = -0.2 + 900

Combine like terms: -0.2 + 900 = 899.8
900 + -60t + t2 = 899.8

Factor a perfect square on the left side:
(t + -30)(t + -30) = 899.8

Calculate the square root of the right side: 29.996666481

Break this problem into two subproblems by setting 
(t + -30) equal to 29.996666481 and -29.996666481.

Subproblem 1

t + -30 = 29.996666481 Simplifying t + -30 = 29.996666481 Reorder the terms: -30 + t = 29.996666481 Solving -30 + t = 29.996666481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = 29.996666481 + 30 Combine like terms: -30 + 30 = 0 0 + t = 29.996666481 + 30 t = 29.996666481 + 30 Combine like terms: 29.996666481 + 30 = 59.996666481 t = 59.996666481 Simplifying t = 59.996666481

Subproblem 2

t + -30 = -29.996666481 Simplifying t + -30 = -29.996666481 Reorder the terms: -30 + t = -29.996666481 Solving -30 + t = -29.996666481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = -29.996666481 + 30 Combine like terms: -30 + 30 = 0 0 + t = -29.996666481 + 30 t = -29.996666481 + 30 Combine like terms: -29.996666481 + 30 = 0.003333519 t = 0.003333519 Simplifying t = 0.003333519

Solution

The solution to the problem is based on the solutions from the subproblems. t = {59.996666481, 0.003333519}

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