5t^2+9t-45=0

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Solution for 5t^2+9t-45=0 equation:


Simplifying
5t2 + 9t + -45 = 0

Reorder the terms:
-45 + 9t + 5t2 = 0

Solving
-45 + 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'.
-9 + 1.8t + t2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 1.8t + 9 + t2 = 0 + 9

Reorder the terms:
-9 + 9 + 1.8t + t2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 1.8t + t2 = 0 + 9
1.8t + t2 = 0 + 9

Combine like terms: 0 + 9 = 9
1.8t + t2 = 9

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 = 9 + 0.81

Reorder the terms:
0.81 + 1.8t + t2 = 9 + 0.81

Combine like terms: 9 + 0.81 = 9.81
0.81 + 1.8t + t2 = 9.81

Factor a perfect square on the left side:
(t + 0.9)(t + 0.9) = 9.81

Calculate the square root of the right side: 3.132091953

Break this problem into two subproblems by setting 
(t + 0.9) equal to 3.132091953 and -3.132091953.

Subproblem 1

t + 0.9 = 3.132091953 Simplifying t + 0.9 = 3.132091953 Reorder the terms: 0.9 + t = 3.132091953 Solving 0.9 + t = 3.132091953 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 = 3.132091953 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + t = 3.132091953 + -0.9 t = 3.132091953 + -0.9 Combine like terms: 3.132091953 + -0.9 = 2.232091953 t = 2.232091953 Simplifying t = 2.232091953

Subproblem 2

t + 0.9 = -3.132091953 Simplifying t + 0.9 = -3.132091953 Reorder the terms: 0.9 + t = -3.132091953 Solving 0.9 + t = -3.132091953 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 = -3.132091953 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + t = -3.132091953 + -0.9 t = -3.132091953 + -0.9 Combine like terms: -3.132091953 + -0.9 = -4.032091953 t = -4.032091953 Simplifying t = -4.032091953

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.232091953, -4.032091953}

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