6t^2+9t=8

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Solution for 6t^2+9t=8 equation:


Simplifying
6t2 + 9t = 8

Reorder the terms:
9t + 6t2 = 8

Solving
9t + 6t2 = 8

Solving for variable 't'.

Reorder the terms:
-8 + 9t + 6t2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 9t + 6t2 = 0

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

Divide each side by '6'.
-1.333333333 + 1.5t + t2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.5t + 1.333333333 + t2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.5t + t2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.5t + t2 = 0 + 1.333333333
1.5t + t2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.5t + t2 = 1.333333333

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 = 1.333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5t + t2 = 1.333333333 + 0.5625

Combine like terms: 1.333333333 + 0.5625 = 1.895833333
0.5625 + 1.5t + t2 = 1.895833333

Factor a perfect square on the left side:
(t + 0.75)(t + 0.75) = 1.895833333

Calculate the square root of the right side: 1.376892637

Break this problem into two subproblems by setting 
(t + 0.75) equal to 1.376892637 and -1.376892637.

Subproblem 1

t + 0.75 = 1.376892637 Simplifying t + 0.75 = 1.376892637 Reorder the terms: 0.75 + t = 1.376892637 Solving 0.75 + t = 1.376892637 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 = 1.376892637 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = 1.376892637 + -0.75 t = 1.376892637 + -0.75 Combine like terms: 1.376892637 + -0.75 = 0.626892637 t = 0.626892637 Simplifying t = 0.626892637

Subproblem 2

t + 0.75 = -1.376892637 Simplifying t + 0.75 = -1.376892637 Reorder the terms: 0.75 + t = -1.376892637 Solving 0.75 + t = -1.376892637 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 = -1.376892637 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = -1.376892637 + -0.75 t = -1.376892637 + -0.75 Combine like terms: -1.376892637 + -0.75 = -2.126892637 t = -2.126892637 Simplifying t = -2.126892637

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.626892637, -2.126892637}

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