8t^2+19t=6

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Solution for 8t^2+19t=6 equation:


Simplifying
8t2 + 19t = 6

Reorder the terms:
19t + 8t2 = 6

Solving
19t + 8t2 = 6

Solving for variable 't'.

Reorder the terms:
-6 + 19t + 8t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 19t + 8t2 = 0

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

Divide each side by '8'.
-0.75 + 2.375t + t2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 2.375t + 0.75 + t2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 2.375t + t2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 2.375t + t2 = 0 + 0.75
2.375t + t2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
2.375t + t2 = 0.75

The t term is 2.375t.  Take half its coefficient (1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
2.375t + 1.41015625 + t2 = 0.75 + 1.41015625

Reorder the terms:
1.41015625 + 2.375t + t2 = 0.75 + 1.41015625

Combine like terms: 0.75 + 1.41015625 = 2.16015625
1.41015625 + 2.375t + t2 = 2.16015625

Factor a perfect square on the left side:
(t + 1.1875)(t + 1.1875) = 2.16015625

Calculate the square root of the right side: 1.469747002

Break this problem into two subproblems by setting 
(t + 1.1875) equal to 1.469747002 and -1.469747002.

Subproblem 1

t + 1.1875 = 1.469747002 Simplifying t + 1.1875 = 1.469747002 Reorder the terms: 1.1875 + t = 1.469747002 Solving 1.1875 + t = 1.469747002 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = 1.469747002 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = 1.469747002 + -1.1875 t = 1.469747002 + -1.1875 Combine like terms: 1.469747002 + -1.1875 = 0.282247002 t = 0.282247002 Simplifying t = 0.282247002

Subproblem 2

t + 1.1875 = -1.469747002 Simplifying t + 1.1875 = -1.469747002 Reorder the terms: 1.1875 + t = -1.469747002 Solving 1.1875 + t = -1.469747002 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = -1.469747002 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = -1.469747002 + -1.1875 t = -1.469747002 + -1.1875 Combine like terms: -1.469747002 + -1.1875 = -2.657247002 t = -2.657247002 Simplifying t = -2.657247002

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.282247002, -2.657247002}

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