60-16t^2=t

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Solution for 60-16t^2=t equation:


Simplifying
60 + -16t2 = t

Solving
60 + -16t2 = t

Solving for variable 't'.

Reorder the terms:
60 + -1t + -16t2 = t + -1t

Combine like terms: t + -1t = 0
60 + -1t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-3.75 + 0.0625t + t2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 0.0625t + 3.75 + t2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 0.0625t + t2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 0.0625t + t2 = 0 + 3.75
0.0625t + t2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
0.0625t + t2 = 3.75

The t term is 0.0625t.  Take half its coefficient (0.03125).
Square it (0.0009765625) and add it to both sides.

Add '0.0009765625' to each side of the equation.
0.0625t + 0.0009765625 + t2 = 3.75 + 0.0009765625

Reorder the terms:
0.0009765625 + 0.0625t + t2 = 3.75 + 0.0009765625

Combine like terms: 3.75 + 0.0009765625 = 3.7509765625
0.0009765625 + 0.0625t + t2 = 3.7509765625

Factor a perfect square on the left side:
(t + 0.03125)(t + 0.03125) = 3.7509765625

Calculate the square root of the right side: 1.936743804

Break this problem into two subproblems by setting 
(t + 0.03125) equal to 1.936743804 and -1.936743804.

Subproblem 1

t + 0.03125 = 1.936743804 Simplifying t + 0.03125 = 1.936743804 Reorder the terms: 0.03125 + t = 1.936743804 Solving 0.03125 + t = 1.936743804 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = 1.936743804 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = 1.936743804 + -0.03125 t = 1.936743804 + -0.03125 Combine like terms: 1.936743804 + -0.03125 = 1.905493804 t = 1.905493804 Simplifying t = 1.905493804

Subproblem 2

t + 0.03125 = -1.936743804 Simplifying t + 0.03125 = -1.936743804 Reorder the terms: 0.03125 + t = -1.936743804 Solving 0.03125 + t = -1.936743804 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = -1.936743804 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = -1.936743804 + -0.03125 t = -1.936743804 + -0.03125 Combine like terms: -1.936743804 + -0.03125 = -1.967993804 t = -1.967993804 Simplifying t = -1.967993804

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.905493804, -1.967993804}

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