t*t+2t-48=12

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Solution for t*t+2t-48=12 equation:


Simplifying
t * t + 2t + -48 = 12

Multiply t * t
t2 + 2t + -48 = 12

Reorder the terms:
-48 + 2t + t2 = 12

Solving
-48 + 2t + t2 = 12

Solving for variable 't'.

Reorder the terms:
-48 + -12 + 2t + t2 = 12 + -12

Combine like terms: -48 + -12 = -60
-60 + 2t + t2 = 12 + -12

Combine like terms: 12 + -12 = 0
-60 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 2t + 60 + t2 = 0 + 60

Reorder the terms:
-60 + 60 + 2t + t2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 2t + t2 = 0 + 60
2t + t2 = 0 + 60

Combine like terms: 0 + 60 = 60
2t + t2 = 60

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 = 60 + 1

Reorder the terms:
1 + 2t + t2 = 60 + 1

Combine like terms: 60 + 1 = 61
1 + 2t + t2 = 61

Factor a perfect square on the left side:
(t + 1)(t + 1) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(t + 1) equal to 7.810249676 and -7.810249676.

Subproblem 1

t + 1 = 7.810249676 Simplifying t + 1 = 7.810249676 Reorder the terms: 1 + t = 7.810249676 Solving 1 + t = 7.810249676 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 = 7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + t = 7.810249676 + -1 t = 7.810249676 + -1 Combine like terms: 7.810249676 + -1 = 6.810249676 t = 6.810249676 Simplifying t = 6.810249676

Subproblem 2

t + 1 = -7.810249676 Simplifying t + 1 = -7.810249676 Reorder the terms: 1 + t = -7.810249676 Solving 1 + t = -7.810249676 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 = -7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + t = -7.810249676 + -1 t = -7.810249676 + -1 Combine like terms: -7.810249676 + -1 = -8.810249676 t = -8.810249676 Simplifying t = -8.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.810249676, -8.810249676}

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