2t^2-3t-48=0

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Solution for 2t^2-3t-48=0 equation:


Simplifying
2t2 + -3t + -48 = 0

Reorder the terms:
-48 + -3t + 2t2 = 0

Solving
-48 + -3t + 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'.
-24 + -1.5t + t2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -1.5t + 24 + t2 = 0 + 24

Reorder the terms:
-24 + 24 + -1.5t + t2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1.5t + t2 = 0 + 24
-1.5t + t2 = 0 + 24

Combine like terms: 0 + 24 = 24
-1.5t + t2 = 24

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 24 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 24 + 0.5625

Combine like terms: 24 + 0.5625 = 24.5625
0.5625 + -1.5t + t2 = 24.5625

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 24.5625

Calculate the square root of the right side: 4.9560569

Break this problem into two subproblems by setting 
(t + -0.75) equal to 4.9560569 and -4.9560569.

Subproblem 1

t + -0.75 = 4.9560569 Simplifying t + -0.75 = 4.9560569 Reorder the terms: -0.75 + t = 4.9560569 Solving -0.75 + t = 4.9560569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 4.9560569 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 4.9560569 + 0.75 t = 4.9560569 + 0.75 Combine like terms: 4.9560569 + 0.75 = 5.7060569 t = 5.7060569 Simplifying t = 5.7060569

Subproblem 2

t + -0.75 = -4.9560569 Simplifying t + -0.75 = -4.9560569 Reorder the terms: -0.75 + t = -4.9560569 Solving -0.75 + t = -4.9560569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -4.9560569 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -4.9560569 + 0.75 t = -4.9560569 + 0.75 Combine like terms: -4.9560569 + 0.75 = -4.2060569 t = -4.2060569 Simplifying t = -4.2060569

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.7060569, -4.2060569}

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