16t^2-33t-30=0

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Solution for 16t^2-33t-30=0 equation:


Simplifying
16t2 + -33t + -30 = 0

Reorder the terms:
-30 + -33t + 16t2 = 0

Solving
-30 + -33t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
-1.875 + -2.0625t + t2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -2.0625t + 1.875 + t2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -2.0625t + t2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -2.0625t + t2 = 0 + 1.875
-2.0625t + t2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-2.0625t + t2 = 1.875

The t term is -2.0625t.  Take half its coefficient (-1.03125).
Square it (1.063476563) and add it to both sides.

Add '1.063476563' to each side of the equation.
-2.0625t + 1.063476563 + t2 = 1.875 + 1.063476563

Reorder the terms:
1.063476563 + -2.0625t + t2 = 1.875 + 1.063476563

Combine like terms: 1.875 + 1.063476563 = 2.938476563
1.063476563 + -2.0625t + t2 = 2.938476563

Factor a perfect square on the left side:
(t + -1.03125)(t + -1.03125) = 2.938476563

Calculate the square root of the right side: 1.714198519

Break this problem into two subproblems by setting 
(t + -1.03125) equal to 1.714198519 and -1.714198519.

Subproblem 1

t + -1.03125 = 1.714198519 Simplifying t + -1.03125 = 1.714198519 Reorder the terms: -1.03125 + t = 1.714198519 Solving -1.03125 + t = 1.714198519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + t = 1.714198519 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = 1.714198519 + 1.03125 t = 1.714198519 + 1.03125 Combine like terms: 1.714198519 + 1.03125 = 2.745448519 t = 2.745448519 Simplifying t = 2.745448519

Subproblem 2

t + -1.03125 = -1.714198519 Simplifying t + -1.03125 = -1.714198519 Reorder the terms: -1.03125 + t = -1.714198519 Solving -1.03125 + t = -1.714198519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + t = -1.714198519 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = -1.714198519 + 1.03125 t = -1.714198519 + 1.03125 Combine like terms: -1.714198519 + 1.03125 = -0.682948519 t = -0.682948519 Simplifying t = -0.682948519

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.745448519, -0.682948519}

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