37t-16t^2=20

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Solution for 37t-16t^2=20 equation:


Simplifying
37t + -16t2 = 20

Solving
37t + -16t2 = 20

Solving for variable 't'.

Reorder the terms:
-20 + 37t + -16t2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 37t + -16t2 = 0

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

Divide each side by '-16'.
1.25 + -2.3125t + t2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.3125t + -1.25 + t2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.3125t + t2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.3125t + t2 = 0 + -1.25
-2.3125t + t2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.3125t + t2 = -1.25

The t term is -2.3125t.  Take half its coefficient (-1.15625).
Square it (1.336914063) and add it to both sides.

Add '1.336914063' to each side of the equation.
-2.3125t + 1.336914063 + t2 = -1.25 + 1.336914063

Reorder the terms:
1.336914063 + -2.3125t + t2 = -1.25 + 1.336914063

Combine like terms: -1.25 + 1.336914063 = 0.086914063
1.336914063 + -2.3125t + t2 = 0.086914063

Factor a perfect square on the left side:
(t + -1.15625)(t + -1.15625) = 0.086914063

Calculate the square root of the right side: 0.294811911

Break this problem into two subproblems by setting 
(t + -1.15625) equal to 0.294811911 and -0.294811911.

Subproblem 1

t + -1.15625 = 0.294811911 Simplifying t + -1.15625 = 0.294811911 Reorder the terms: -1.15625 + t = 0.294811911 Solving -1.15625 + t = 0.294811911 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + t = 0.294811911 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + t = 0.294811911 + 1.15625 t = 0.294811911 + 1.15625 Combine like terms: 0.294811911 + 1.15625 = 1.451061911 t = 1.451061911 Simplifying t = 1.451061911

Subproblem 2

t + -1.15625 = -0.294811911 Simplifying t + -1.15625 = -0.294811911 Reorder the terms: -1.15625 + t = -0.294811911 Solving -1.15625 + t = -0.294811911 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + t = -0.294811911 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + t = -0.294811911 + 1.15625 t = -0.294811911 + 1.15625 Combine like terms: -0.294811911 + 1.15625 = 0.861438089 t = 0.861438089 Simplifying t = 0.861438089

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.451061911, 0.861438089}

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