.5t^2-3t-8=0

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Solution for .5t^2-3t-8=0 equation:


Simplifying
0.5t2 + -3t + -8 = 0

Reorder the terms:
-8 + -3t + 0.5t2 = 0

Solving
-8 + -3t + 0.5t2 = 0

Solving for variable 't'.

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

Divide each side by '0.5'.
-16 + -6t + t2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -6t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + -6t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -6t + t2 = 0 + 16
-6t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
-6t + t2 = 16

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 16 + 9

Reorder the terms:
9 + -6t + t2 = 16 + 9

Combine like terms: 16 + 9 = 25
9 + -6t + t2 = 25

Factor a perfect square on the left side:
(t + -3)(t + -3) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(t + -3) equal to 5 and -5.

Subproblem 1

t + -3 = 5 Simplifying t + -3 = 5 Reorder the terms: -3 + t = 5 Solving -3 + t = 5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 5 + 3 Combine like terms: -3 + 3 = 0 0 + t = 5 + 3 t = 5 + 3 Combine like terms: 5 + 3 = 8 t = 8 Simplifying t = 8

Subproblem 2

t + -3 = -5 Simplifying t + -3 = -5 Reorder the terms: -3 + t = -5 Solving -3 + t = -5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -5 + 3 Combine like terms: -3 + 3 = 0 0 + t = -5 + 3 t = -5 + 3 Combine like terms: -5 + 3 = -2 t = -2 Simplifying t = -2

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8, -2}

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