=2T^2+3T-4

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Solution for =2T^2+3T-4 equation:


Simplifying
0 = 2T2 + 3T + -4

Reorder the terms:
0 = -4 + 3T + 2T2

Solving
0 = -4 + 3T + 2T2

Solving for variable 'T'.

Combine like terms: 0 + 4 = 4
4 + -3T + -2T2 = -4 + 3T + 2T2 + 4 + -3T + -2T2

Reorder the terms:
4 + -3T + -2T2 = -4 + 4 + 3T + -3T + 2T2 + -2T2

Combine like terms: -4 + 4 = 0
4 + -3T + -2T2 = 0 + 3T + -3T + 2T2 + -2T2
4 + -3T + -2T2 = 3T + -3T + 2T2 + -2T2

Combine like terms: 3T + -3T = 0
4 + -3T + -2T2 = 0 + 2T2 + -2T2
4 + -3T + -2T2 = 2T2 + -2T2

Combine like terms: 2T2 + -2T2 = 0
4 + -3T + -2T2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-2 + 1.5T + T2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.5T + 2 + T2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.5T + T2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.5T + T2 = 0 + 2
1.5T + T2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.5T + T2 = 2

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 = 2 + 0.5625

Reorder the terms:
0.5625 + 1.5T + T2 = 2 + 0.5625

Combine like terms: 2 + 0.5625 = 2.5625
0.5625 + 1.5T + T2 = 2.5625

Factor a perfect square on the left side:
(T + 0.75)(T + 0.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(T + 0.75) equal to 1.600781059 and -1.600781059.

Subproblem 1

T + 0.75 = 1.600781059 Simplifying T + 0.75 = 1.600781059 Reorder the terms: 0.75 + T = 1.600781059 Solving 0.75 + T = 1.600781059 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 = 1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + T = 1.600781059 + -0.75 T = 1.600781059 + -0.75 Combine like terms: 1.600781059 + -0.75 = 0.850781059 T = 0.850781059 Simplifying T = 0.850781059

Subproblem 2

T + 0.75 = -1.600781059 Simplifying T + 0.75 = -1.600781059 Reorder the terms: 0.75 + T = -1.600781059 Solving 0.75 + T = -1.600781059 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 = -1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + T = -1.600781059 + -0.75 T = -1.600781059 + -0.75 Combine like terms: -1.600781059 + -0.75 = -2.350781059 T = -2.350781059 Simplifying T = -2.350781059

Solution

The solution to the problem is based on the solutions from the subproblems. T = {0.850781059, -2.350781059}

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