-4.9t^2+49t+5=0

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Solution for -4.9t^2+49t+5=0 equation:


Simplifying
-4.9t2 + 49t + 5 = 0

Reorder the terms:
5 + 49t + -4.9t2 = 0

Solving
5 + 49t + -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'.
-1.020408163 + -10t + t2 = 0

Move the constant term to the right:

Add '1.020408163' to each side of the equation.
-1.020408163 + -10t + 1.020408163 + t2 = 0 + 1.020408163

Reorder the terms:
-1.020408163 + 1.020408163 + -10t + t2 = 0 + 1.020408163

Combine like terms: -1.020408163 + 1.020408163 = 0.000000000
0.000000000 + -10t + t2 = 0 + 1.020408163
-10t + t2 = 0 + 1.020408163

Combine like terms: 0 + 1.020408163 = 1.020408163
-10t + t2 = 1.020408163

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = 1.020408163 + 25

Reorder the terms:
25 + -10t + t2 = 1.020408163 + 25

Combine like terms: 1.020408163 + 25 = 26.020408163
25 + -10t + t2 = 26.020408163

Factor a perfect square on the left side:
(t + -5)(t + -5) = 26.020408163

Calculate the square root of the right side: 5.101020306

Break this problem into two subproblems by setting 
(t + -5) equal to 5.101020306 and -5.101020306.

Subproblem 1

t + -5 = 5.101020306 Simplifying t + -5 = 5.101020306 Reorder the terms: -5 + t = 5.101020306 Solving -5 + t = 5.101020306 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.101020306 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.101020306 + 5 t = 5.101020306 + 5 Combine like terms: 5.101020306 + 5 = 10.101020306 t = 10.101020306 Simplifying t = 10.101020306

Subproblem 2

t + -5 = -5.101020306 Simplifying t + -5 = -5.101020306 Reorder the terms: -5 + t = -5.101020306 Solving -5 + t = -5.101020306 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.101020306 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.101020306 + 5 t = -5.101020306 + 5 Combine like terms: -5.101020306 + 5 = -0.101020306 t = -0.101020306 Simplifying t = -0.101020306

Solution

The solution to the problem is based on the solutions from the subproblems. t = {10.101020306, -0.101020306}

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