22t+9.81t^2-10=0

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Solution for 22t+9.81t^2-10=0 equation:


Simplifying
22t + 9.81t2 + -10 = 0

Reorder the terms:
-10 + 22t + 9.81t2 = 0

Solving
-10 + 22t + 9.81t2 = 0

Solving for variable 't'.

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

Divide each side by '9.81'.
-1.019367992 + 2.242609582t + t2 = 0

Move the constant term to the right:

Add '1.019367992' to each side of the equation.
-1.019367992 + 2.242609582t + 1.019367992 + t2 = 0 + 1.019367992

Reorder the terms:
-1.019367992 + 1.019367992 + 2.242609582t + t2 = 0 + 1.019367992

Combine like terms: -1.019367992 + 1.019367992 = 0.000000000
0.000000000 + 2.242609582t + t2 = 0 + 1.019367992
2.242609582t + t2 = 0 + 1.019367992

Combine like terms: 0 + 1.019367992 = 1.019367992
2.242609582t + t2 = 1.019367992

The t term is 2.242609582t.  Take half its coefficient (1.121304791).
Square it (1.257324434) and add it to both sides.

Add '1.257324434' to each side of the equation.
2.242609582t + 1.257324434 + t2 = 1.019367992 + 1.257324434

Reorder the terms:
1.257324434 + 2.242609582t + t2 = 1.019367992 + 1.257324434

Combine like terms: 1.019367992 + 1.257324434 = 2.276692426
1.257324434 + 2.242609582t + t2 = 2.276692426

Factor a perfect square on the left side:
(t + 1.121304791)(t + 1.121304791) = 2.276692426

Calculate the square root of the right side: 1.508871242

Break this problem into two subproblems by setting 
(t + 1.121304791) equal to 1.508871242 and -1.508871242.

Subproblem 1

t + 1.121304791 = 1.508871242 Simplifying t + 1.121304791 = 1.508871242 Reorder the terms: 1.121304791 + t = 1.508871242 Solving 1.121304791 + t = 1.508871242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.121304791' to each side of the equation. 1.121304791 + -1.121304791 + t = 1.508871242 + -1.121304791 Combine like terms: 1.121304791 + -1.121304791 = 0.000000000 0.000000000 + t = 1.508871242 + -1.121304791 t = 1.508871242 + -1.121304791 Combine like terms: 1.508871242 + -1.121304791 = 0.387566451 t = 0.387566451 Simplifying t = 0.387566451

Subproblem 2

t + 1.121304791 = -1.508871242 Simplifying t + 1.121304791 = -1.508871242 Reorder the terms: 1.121304791 + t = -1.508871242 Solving 1.121304791 + t = -1.508871242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.121304791' to each side of the equation. 1.121304791 + -1.121304791 + t = -1.508871242 + -1.121304791 Combine like terms: 1.121304791 + -1.121304791 = 0.000000000 0.000000000 + t = -1.508871242 + -1.121304791 t = -1.508871242 + -1.121304791 Combine like terms: -1.508871242 + -1.121304791 = -2.630176033 t = -2.630176033 Simplifying t = -2.630176033

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.387566451, -2.630176033}

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