4.9t^2-29.4t-39.2=0

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Solution for 4.9t^2-29.4t-39.2=0 equation:


Simplifying
4.9t2 + -29.4t + -39.2 = 0

Reorder the terms:
-39.2 + -29.4t + 4.9t2 = 0

Solving
-39.2 + -29.4t + 4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '4.9'.
-8 + -6t + t2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -6t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + -6t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -6t + t2 = 0 + 8
-6t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
-6t + t2 = 8

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 8 + 9

Reorder the terms:
9 + -6t + t2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + -6t + t2 = 17

Factor a perfect square on the left side:
(t + -3)(t + -3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(t + -3) equal to 4.123105626 and -4.123105626.

Subproblem 1

t + -3 = 4.123105626 Simplifying t + -3 = 4.123105626 Reorder the terms: -3 + t = 4.123105626 Solving -3 + t = 4.123105626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.123105626 + 3 t = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 t = 7.123105626 Simplifying t = 7.123105626

Subproblem 2

t + -3 = -4.123105626 Simplifying t + -3 = -4.123105626 Reorder the terms: -3 + t = -4.123105626 Solving -3 + t = -4.123105626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.123105626 + 3 t = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 t = -1.123105626 Simplifying t = -1.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.123105626, -1.123105626}

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