4t^2+-37t+18=0

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Solution for 4t^2+-37t+18=0 equation:


Simplifying
4t2 + -37t + 18 = 0

Reorder the terms:
18 + -37t + 4t2 = 0

Solving
18 + -37t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
4.5 + -9.25t + t2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -9.25t + -4.5 + t2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -9.25t + t2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -9.25t + t2 = 0 + -4.5
-9.25t + t2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-9.25t + t2 = -4.5

The t term is -9.25t.  Take half its coefficient (-4.625).
Square it (21.390625) and add it to both sides.

Add '21.390625' to each side of the equation.
-9.25t + 21.390625 + t2 = -4.5 + 21.390625

Reorder the terms:
21.390625 + -9.25t + t2 = -4.5 + 21.390625

Combine like terms: -4.5 + 21.390625 = 16.890625
21.390625 + -9.25t + t2 = 16.890625

Factor a perfect square on the left side:
(t + -4.625)(t + -4.625) = 16.890625

Calculate the square root of the right side: 4.109820556

Break this problem into two subproblems by setting 
(t + -4.625) equal to 4.109820556 and -4.109820556.

Subproblem 1

t + -4.625 = 4.109820556 Simplifying t + -4.625 = 4.109820556 Reorder the terms: -4.625 + t = 4.109820556 Solving -4.625 + t = 4.109820556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + t = 4.109820556 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + t = 4.109820556 + 4.625 t = 4.109820556 + 4.625 Combine like terms: 4.109820556 + 4.625 = 8.734820556 t = 8.734820556 Simplifying t = 8.734820556

Subproblem 2

t + -4.625 = -4.109820556 Simplifying t + -4.625 = -4.109820556 Reorder the terms: -4.625 + t = -4.109820556 Solving -4.625 + t = -4.109820556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + t = -4.109820556 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + t = -4.109820556 + 4.625 t = -4.109820556 + 4.625 Combine like terms: -4.109820556 + 4.625 = 0.515179444 t = 0.515179444 Simplifying t = 0.515179444

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.734820556, 0.515179444}

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