3t^2-4t-36=0

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Solution for 3t^2-4t-36=0 equation:


Simplifying
3t2 + -4t + -36 = 0

Reorder the terms:
-36 + -4t + 3t2 = 0

Solving
-36 + -4t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
-12 + -1.333333333t + t2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -1.333333333t + 12 + t2 = 0 + 12

Reorder the terms:
-12 + 12 + -1.333333333t + t2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1.333333333t + t2 = 0 + 12
-1.333333333t + t2 = 0 + 12

Combine like terms: 0 + 12 = 12
-1.333333333t + t2 = 12

The t term is -1.333333333t.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333t + 0.4444444442 + t2 = 12 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333t + t2 = 12 + 0.4444444442

Combine like terms: 12 + 0.4444444442 = 12.4444444442
0.4444444442 + -1.333333333t + t2 = 12.4444444442

Factor a perfect square on the left side:
(t + -0.6666666665)(t + -0.6666666665) = 12.4444444442

Calculate the square root of the right side: 3.527668415

Break this problem into two subproblems by setting 
(t + -0.6666666665) equal to 3.527668415 and -3.527668415.

Subproblem 1

t + -0.6666666665 = 3.527668415 Simplifying t + -0.6666666665 = 3.527668415 Reorder the terms: -0.6666666665 + t = 3.527668415 Solving -0.6666666665 + t = 3.527668415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + t = 3.527668415 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + t = 3.527668415 + 0.6666666665 t = 3.527668415 + 0.6666666665 Combine like terms: 3.527668415 + 0.6666666665 = 4.1943350815 t = 4.1943350815 Simplifying t = 4.1943350815

Subproblem 2

t + -0.6666666665 = -3.527668415 Simplifying t + -0.6666666665 = -3.527668415 Reorder the terms: -0.6666666665 + t = -3.527668415 Solving -0.6666666665 + t = -3.527668415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + t = -3.527668415 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + t = -3.527668415 + 0.6666666665 t = -3.527668415 + 0.6666666665 Combine like terms: -3.527668415 + 0.6666666665 = -2.8610017485 t = -2.8610017485 Simplifying t = -2.8610017485

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.1943350815, -2.8610017485}

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