(t^2)+2t-44=0

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Solution for (t^2)+2t-44=0 equation:


Simplifying
(t2) + 2t + -44 = 0
t2 + 2t + -44 = 0

Reorder the terms:
-44 + 2t + t2 = 0

Solving
-44 + 2t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 2t + 44 + t2 = 0 + 44

Reorder the terms:
-44 + 44 + 2t + t2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 2t + t2 = 0 + 44
2t + t2 = 0 + 44

Combine like terms: 0 + 44 = 44
2t + t2 = 44

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 44 + 1

Reorder the terms:
1 + 2t + t2 = 44 + 1

Combine like terms: 44 + 1 = 45
1 + 2t + t2 = 45

Factor a perfect square on the left side:
(t + 1)(t + 1) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(t + 1) equal to 6.708203933 and -6.708203933.

Subproblem 1

t + 1 = 6.708203933 Simplifying t + 1 = 6.708203933 Reorder the terms: 1 + t = 6.708203933 Solving 1 + t = 6.708203933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + t = 6.708203933 + -1 t = 6.708203933 + -1 Combine like terms: 6.708203933 + -1 = 5.708203933 t = 5.708203933 Simplifying t = 5.708203933

Subproblem 2

t + 1 = -6.708203933 Simplifying t + 1 = -6.708203933 Reorder the terms: 1 + t = -6.708203933 Solving 1 + t = -6.708203933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + t = -6.708203933 + -1 t = -6.708203933 + -1 Combine like terms: -6.708203933 + -1 = -7.708203933 t = -7.708203933 Simplifying t = -7.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.708203933, -7.708203933}

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