1+9t+5t^2=0

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Solution for 1+9t+5t^2=0 equation:


Simplifying
1 + 9t + 5t2 = 0

Solving
1 + 9t + 5t2 = 0

Solving for variable 't'.

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 = 0.61
0.81 + 1.8t + t2 = 0.61

Factor a perfect square on the left side:
(t + 0.9)(t + 0.9) = 0.61

Calculate the square root of the right side: 0.781024968

Break this problem into two subproblems by setting 
(t + 0.9) equal to 0.781024968 and -0.781024968.

Subproblem 1

t + 0.9 = 0.781024968 Simplifying t + 0.9 = 0.781024968 Reorder the terms: 0.9 + t = 0.781024968 Solving 0.9 + t = 0.781024968 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 = 0.781024968 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + t = 0.781024968 + -0.9 t = 0.781024968 + -0.9 Combine like terms: 0.781024968 + -0.9 = -0.118975032 t = -0.118975032 Simplifying t = -0.118975032

Subproblem 2

t + 0.9 = -0.781024968 Simplifying t + 0.9 = -0.781024968 Reorder the terms: 0.9 + t = -0.781024968 Solving 0.9 + t = -0.781024968 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 = -0.781024968 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + t = -0.781024968 + -0.9 t = -0.781024968 + -0.9 Combine like terms: -0.781024968 + -0.9 = -1.681024968 t = -1.681024968 Simplifying t = -1.681024968

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.118975032, -1.681024968}

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