-5t(t-2)+8t=9t-8

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Solution for -5t(t-2)+8t=9t-8 equation:


Simplifying
-5t(t + -2) + 8t = 9t + -8

Reorder the terms:
-5t(-2 + t) + 8t = 9t + -8
(-2 * -5t + t * -5t) + 8t = 9t + -8
(10t + -5t2) + 8t = 9t + -8

Reorder the terms:
10t + 8t + -5t2 = 9t + -8

Combine like terms: 10t + 8t = 18t
18t + -5t2 = 9t + -8

Reorder the terms:
18t + -5t2 = -8 + 9t

Solving
18t + -5t2 = -8 + 9t

Solving for variable 't'.

Reorder the terms:
8 + 18t + -9t + -5t2 = -8 + 9t + 8 + -9t

Combine like terms: 18t + -9t = 9t
8 + 9t + -5t2 = -8 + 9t + 8 + -9t

Reorder the terms:
8 + 9t + -5t2 = -8 + 8 + 9t + -9t

Combine like terms: -8 + 8 = 0
8 + 9t + -5t2 = 0 + 9t + -9t
8 + 9t + -5t2 = 9t + -9t

Combine like terms: 9t + -9t = 0
8 + 9t + -5t2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.6 + -1.8t + t2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -1.8t + 1.6 + t2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -1.8t + t2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -1.8t + t2 = 0 + 1.6
-1.8t + t2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-1.8t + t2 = 1.6

The t term is -1.8t.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8t + 0.81 + t2 = 1.6 + 0.81

Reorder the terms:
0.81 + -1.8t + t2 = 1.6 + 0.81

Combine like terms: 1.6 + 0.81 = 2.41
0.81 + -1.8t + t2 = 2.41

Factor a perfect square on the left side:
(t + -0.9)(t + -0.9) = 2.41

Calculate the square root of the right side: 1.55241747

Break this problem into two subproblems by setting 
(t + -0.9) equal to 1.55241747 and -1.55241747.

Subproblem 1

t + -0.9 = 1.55241747 Simplifying t + -0.9 = 1.55241747 Reorder the terms: -0.9 + t = 1.55241747 Solving -0.9 + t = 1.55241747 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + t = 1.55241747 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = 1.55241747 + 0.9 t = 1.55241747 + 0.9 Combine like terms: 1.55241747 + 0.9 = 2.45241747 t = 2.45241747 Simplifying t = 2.45241747

Subproblem 2

t + -0.9 = -1.55241747 Simplifying t + -0.9 = -1.55241747 Reorder the terms: -0.9 + t = -1.55241747 Solving -0.9 + t = -1.55241747 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + t = -1.55241747 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = -1.55241747 + 0.9 t = -1.55241747 + 0.9 Combine like terms: -1.55241747 + 0.9 = -0.65241747 t = -0.65241747 Simplifying t = -0.65241747

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.45241747, -0.65241747}

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