2t^2+5t-8=0

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Solution for 2t^2+5t-8=0 equation:


Simplifying
2t2 + 5t + -8 = 0

Reorder the terms:
-8 + 5t + 2t2 = 0

Solving
-8 + 5t + 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 + 2.5t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2.5t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 2.5t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2.5t + t2 = 0 + 4
2.5t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
2.5t + t2 = 4

The t term is 2.5t.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5t + 1.5625 + t2 = 4 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + 2.5t + t2 = 5.5625

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(t + 1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1

t + 1.25 = 2.358495283 Simplifying t + 1.25 = 2.358495283 Reorder the terms: 1.25 + t = 2.358495283 Solving 1.25 + t = 2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 2.358495283 + -1.25 t = 2.358495283 + -1.25 Combine like terms: 2.358495283 + -1.25 = 1.108495283 t = 1.108495283 Simplifying t = 1.108495283

Subproblem 2

t + 1.25 = -2.358495283 Simplifying t + 1.25 = -2.358495283 Reorder the terms: 1.25 + t = -2.358495283 Solving 1.25 + t = -2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -2.358495283 + -1.25 t = -2.358495283 + -1.25 Combine like terms: -2.358495283 + -1.25 = -3.608495283 t = -3.608495283 Simplifying t = -3.608495283

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.108495283, -3.608495283}

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