-9.8t^2+20t+35=0

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Solution for -9.8t^2+20t+35=0 equation:


Simplifying
-9.8t2 + 20t + 35 = 0

Reorder the terms:
35 + 20t + -9.8t2 = 0

Solving
35 + 20t + -9.8t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-9.8 the coefficient of the squared term: 

Divide each side by '-9.8'.
-3.571428571 + -2.040816327t + t2 = 0

Move the constant term to the right:

Add '3.571428571' to each side of the equation.
-3.571428571 + -2.040816327t + 3.571428571 + t2 = 0 + 3.571428571

Reorder the terms:
-3.571428571 + 3.571428571 + -2.040816327t + t2 = 0 + 3.571428571

Combine like terms: -3.571428571 + 3.571428571 = 0.000000000
0.000000000 + -2.040816327t + t2 = 0 + 3.571428571
-2.040816327t + t2 = 0 + 3.571428571

Combine like terms: 0 + 3.571428571 = 3.571428571
-2.040816327t + t2 = 3.571428571

The t term is -2.040816327t.  Take half its coefficient (-1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
-2.040816327t + 1.041232821 + t2 = 3.571428571 + 1.041232821

Reorder the terms:
1.041232821 + -2.040816327t + t2 = 3.571428571 + 1.041232821

Combine like terms: 3.571428571 + 1.041232821 = 4.612661392
1.041232821 + -2.040816327t + t2 = 4.612661392

Factor a perfect square on the left side:
(t + -1.020408164)(t + -1.020408164) = 4.612661392

Calculate the square root of the right side: 2.147710733

Break this problem into two subproblems by setting 
(t + -1.020408164) equal to 2.147710733 and -2.147710733.

Subproblem 1

t + -1.020408164 = 2.147710733 Simplifying t + -1.020408164 = 2.147710733 Reorder the terms: -1.020408164 + t = 2.147710733 Solving -1.020408164 + t = 2.147710733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 2.147710733 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 2.147710733 + 1.020408164 t = 2.147710733 + 1.020408164 Combine like terms: 2.147710733 + 1.020408164 = 3.168118897 t = 3.168118897 Simplifying t = 3.168118897

Subproblem 2

t + -1.020408164 = -2.147710733 Simplifying t + -1.020408164 = -2.147710733 Reorder the terms: -1.020408164 + t = -2.147710733 Solving -1.020408164 + t = -2.147710733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -2.147710733 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -2.147710733 + 1.020408164 t = -2.147710733 + 1.020408164 Combine like terms: -2.147710733 + 1.020408164 = -1.127302569 t = -1.127302569 Simplifying t = -1.127302569

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.168118897, -1.127302569}

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