2t^2-7t-8=0

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Solution for 2t^2-7t-8=0 equation:


Simplifying
2t2 + -7t + -8 = 0

Reorder the terms:
-8 + -7t + 2t2 = 0

Solving
-8 + -7t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
-4 + -3.5t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -3.5t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + -3.5t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3.5t + t2 = 0 + 4
-3.5t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
-3.5t + t2 = 4

The t term is -3.5t.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5t + 3.0625 + t2 = 4 + 3.0625

Reorder the terms:
3.0625 + -3.5t + t2 = 4 + 3.0625

Combine like terms: 4 + 3.0625 = 7.0625
3.0625 + -3.5t + t2 = 7.0625

Factor a perfect square on the left side:
(t + -1.75)(t + -1.75) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(t + -1.75) equal to 2.657536453 and -2.657536453.

Subproblem 1

t + -1.75 = 2.657536453 Simplifying t + -1.75 = 2.657536453 Reorder the terms: -1.75 + t = 2.657536453 Solving -1.75 + t = 2.657536453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = 2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 2.657536453 + 1.75 t = 2.657536453 + 1.75 Combine like terms: 2.657536453 + 1.75 = 4.407536453 t = 4.407536453 Simplifying t = 4.407536453

Subproblem 2

t + -1.75 = -2.657536453 Simplifying t + -1.75 = -2.657536453 Reorder the terms: -1.75 + t = -2.657536453 Solving -1.75 + t = -2.657536453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = -2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -2.657536453 + 1.75 t = -2.657536453 + 1.75 Combine like terms: -2.657536453 + 1.75 = -0.907536453 t = -0.907536453 Simplifying t = -0.907536453

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.407536453, -0.907536453}

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