2t^2-10t-25=0

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Solution for 2t^2-10t-25=0 equation:


Simplifying
2t2 + -10t + -25 = 0

Reorder the terms:
-25 + -10t + 2t2 = 0

Solving
-25 + -10t + 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'.
-12.5 + -5t + t2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -5t + 12.5 + t2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -5t + t2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -5t + t2 = 0 + 12.5
-5t + t2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-5t + t2 = 12.5

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = 12.5 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 12.5 + 6.25

Combine like terms: 12.5 + 6.25 = 18.75
6.25 + -5t + t2 = 18.75

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 18.75

Calculate the square root of the right side: 4.330127019

Break this problem into two subproblems by setting 
(t + -2.5) equal to 4.330127019 and -4.330127019.

Subproblem 1

t + -2.5 = 4.330127019 Simplifying t + -2.5 = 4.330127019 Reorder the terms: -2.5 + t = 4.330127019 Solving -2.5 + t = 4.330127019 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 4.330127019 + 2.5 t = 4.330127019 + 2.5 Combine like terms: 4.330127019 + 2.5 = 6.830127019 t = 6.830127019 Simplifying t = 6.830127019

Subproblem 2

t + -2.5 = -4.330127019 Simplifying t + -2.5 = -4.330127019 Reorder the terms: -2.5 + t = -4.330127019 Solving -2.5 + t = -4.330127019 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -4.330127019 + 2.5 t = -4.330127019 + 2.5 Combine like terms: -4.330127019 + 2.5 = -1.830127019 t = -1.830127019 Simplifying t = -1.830127019

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.830127019, -1.830127019}

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