2t^2-5t-9=0

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Solution for 2t^2-5t-9=0 equation:


Simplifying
2t2 + -5t + -9 = 0

Reorder the terms:
-9 + -5t + 2t2 = 0

Solving
-9 + -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'.
-4.5 + -2.5t + t2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -2.5t + 4.5 + t2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -2.5t + t2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -2.5t + t2 = 0 + 4.5
-2.5t + t2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-2.5t + t2 = 4.5

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 = 4.5 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = 4.5 + 1.5625

Combine like terms: 4.5 + 1.5625 = 6.0625
1.5625 + -2.5t + t2 = 6.0625

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(t + -1.25) equal to 2.46221445 and -2.46221445.

Subproblem 1

t + -1.25 = 2.46221445 Simplifying t + -1.25 = 2.46221445 Reorder the terms: -1.25 + t = 2.46221445 Solving -1.25 + t = 2.46221445 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 = 2.46221445 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 2.46221445 + 1.25 t = 2.46221445 + 1.25 Combine like terms: 2.46221445 + 1.25 = 3.71221445 t = 3.71221445 Simplifying t = 3.71221445

Subproblem 2

t + -1.25 = -2.46221445 Simplifying t + -1.25 = -2.46221445 Reorder the terms: -1.25 + t = -2.46221445 Solving -1.25 + t = -2.46221445 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 = -2.46221445 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -2.46221445 + 1.25 t = -2.46221445 + 1.25 Combine like terms: -2.46221445 + 1.25 = -1.21221445 t = -1.21221445 Simplifying t = -1.21221445

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.71221445, -1.21221445}

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