5t^2-9t+1=2

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Solution for 5t^2-9t+1=2 equation:


Simplifying
5t2 + -9t + 1 = 2

Reorder the terms:
1 + -9t + 5t2 = 2

Solving
1 + -9t + 5t2 = 2

Solving for variable 't'.

Reorder the terms:
1 + -2 + -9t + 5t2 = 2 + -2

Combine like terms: 1 + -2 = -1
-1 + -9t + 5t2 = 2 + -2

Combine like terms: 2 + -2 = 0
-1 + -9t + 5t2 = 0

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

Divide each side by '5'.
-0.2 + -1.8t + t2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.8t + 0.2 + t2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.8t + t2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.8t + t2 = 0 + 0.2
-1.8t + t2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-1.8t + t2 = 0.2

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 = 0.2 + 0.81

Reorder the terms:
0.81 + -1.8t + t2 = 0.2 + 0.81

Combine like terms: 0.2 + 0.81 = 1.01
0.81 + -1.8t + t2 = 1.01

Factor a perfect square on the left side:
(t + -0.9)(t + -0.9) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(t + -0.9) equal to 1.004987562 and -1.004987562.

Subproblem 1

t + -0.9 = 1.004987562 Simplifying t + -0.9 = 1.004987562 Reorder the terms: -0.9 + t = 1.004987562 Solving -0.9 + t = 1.004987562 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 = 1.004987562 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = 1.004987562 + 0.9 t = 1.004987562 + 0.9 Combine like terms: 1.004987562 + 0.9 = 1.904987562 t = 1.904987562 Simplifying t = 1.904987562

Subproblem 2

t + -0.9 = -1.004987562 Simplifying t + -0.9 = -1.004987562 Reorder the terms: -0.9 + t = -1.004987562 Solving -0.9 + t = -1.004987562 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 = -1.004987562 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = -1.004987562 + 0.9 t = -1.004987562 + 0.9 Combine like terms: -1.004987562 + 0.9 = -0.104987562 t = -0.104987562 Simplifying t = -0.104987562

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.904987562, -0.104987562}

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