3t^2+5t-16=4

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Solution for 3t^2+5t-16=4 equation: 


Simplifying
3t2 + 5t + -16 = 4

Reorder the terms:
-16 + 5t + 3t2 = 4

Solving
-16 + 5t + 3t2 = 4

Solving for variable 't'.

Reorder the terms:
-16 + -4 + 5t + 3t2 = 4 + -4

Combine like terms: -16 + -4 = -20
-20 + 5t + 3t2 = 4 + -4

Combine like terms: 4 + -4 = 0
-20 + 5t + 3t2 = 0

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

Divide each side by '3'.
-6.666666667 + 1.666666667t + t2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 1.666666667t + 6.666666667 + t2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 1.666666667t + t2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 1.666666667t + t2 = 0 + 6.666666667
1.666666667t + t2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
1.666666667t + t2 = 6.666666667

The t term is 1.666666667t.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667t + 0.6944444447 + t2 = 6.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667t + t2 = 6.666666667 + 0.6944444447

Combine like terms: 6.666666667 + 0.6944444447 = 7.3611111117
0.6944444447 + 1.666666667t + t2 = 7.3611111117

Factor a perfect square on the left side:
(t + 0.8333333335)(t + 0.8333333335) = 7.3611111117

Calculate the square root of the right side: 2.713136766

Break this problem into two subproblems by setting 
(t + 0.8333333335) equal to 2.713136766 and -2.713136766.


Subproblem 1
t + 0.8333333335 = 2.713136766

Simplifying
t + 0.8333333335 = 2.713136766

Reorder the terms:
0.8333333335 + t = 2.713136766

Solving
0.8333333335 + t = 2.713136766

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + t = 2.713136766 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + t = 2.713136766 + -0.8333333335
t = 2.713136766 + -0.8333333335

Combine like terms: 2.713136766 + -0.8333333335 = 1.8798034325
t = 1.8798034325

Simplifying
t = 1.8798034325


Subproblem 2
t + 0.8333333335 = -2.713136766

Simplifying
t + 0.8333333335 = -2.713136766

Reorder the terms:
0.8333333335 + t = -2.713136766

Solving
0.8333333335 + t = -2.713136766

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + t = -2.713136766 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + t = -2.713136766 + -0.8333333335
t = -2.713136766 + -0.8333333335

Combine like terms: -2.713136766 + -0.8333333335 = -3.5464700995
t = -3.5464700995

Simplifying
t = -3.5464700995


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.8798034325, -3.5464700995}

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