2t^2-8t-15=0

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Solution for 2t^2-8t-15=0 equation:


Simplifying
2t2 + -8t + -15 = 0

Reorder the terms:
-15 + -8t + 2t2 = 0

Solving
-15 + -8t + 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'.
-7.5 + -4t + t2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -4t + 7.5 + t2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -4t + t2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -4t + t2 = 0 + 7.5
-4t + t2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-4t + t2 = 7.5

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 7.5 + 4

Reorder the terms:
4 + -4t + t2 = 7.5 + 4

Combine like terms: 7.5 + 4 = 11.5
4 + -4t + t2 = 11.5

Factor a perfect square on the left side:
(t + -2)(t + -2) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(t + -2) equal to 3.391164992 and -3.391164992.

Subproblem 1

t + -2 = 3.391164992 Simplifying t + -2 = 3.391164992 Reorder the terms: -2 + t = 3.391164992 Solving -2 + t = 3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.391164992 + 2 t = 3.391164992 + 2 Combine like terms: 3.391164992 + 2 = 5.391164992 t = 5.391164992 Simplifying t = 5.391164992

Subproblem 2

t + -2 = -3.391164992 Simplifying t + -2 = -3.391164992 Reorder the terms: -2 + t = -3.391164992 Solving -2 + t = -3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.391164992 + 2 t = -3.391164992 + 2 Combine like terms: -3.391164992 + 2 = -1.391164992 t = -1.391164992 Simplifying t = -1.391164992

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.391164992, -1.391164992}

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