-4.905t^2-t+10=0

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Solution for -4.905t^2-t+10=0 equation:


Simplifying
-4.905t2 + -1t + 10 = 0

Reorder the terms:
10 + -1t + -4.905t2 = 0

Solving
10 + -1t + -4.905t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4.905 the coefficient of the squared term: 

Divide each side by '-4.905'.
-2.038735984 + 0.2038735984t + t2 = 0

Move the constant term to the right:

Add '2.038735984' to each side of the equation.
-2.038735984 + 0.2038735984t + 2.038735984 + t2 = 0 + 2.038735984

Reorder the terms:
-2.038735984 + 2.038735984 + 0.2038735984t + t2 = 0 + 2.038735984

Combine like terms: -2.038735984 + 2.038735984 = 0.000000000
0.000000000 + 0.2038735984t + t2 = 0 + 2.038735984
0.2038735984t + t2 = 0 + 2.038735984

Combine like terms: 0 + 2.038735984 = 2.038735984
0.2038735984t + t2 = 2.038735984

The t term is 0.2038735984t.  Take half its coefficient (0.1019367992).
Square it (0.01039111103) and add it to both sides.

Add '0.01039111103' to each side of the equation.
0.2038735984t + 0.01039111103 + t2 = 2.038735984 + 0.01039111103

Reorder the terms:
0.01039111103 + 0.2038735984t + t2 = 2.038735984 + 0.01039111103

Combine like terms: 2.038735984 + 0.01039111103 = 2.04912709503
0.01039111103 + 0.2038735984t + t2 = 2.04912709503

Factor a perfect square on the left side:
(t + 0.1019367992)(t + 0.1019367992) = 2.04912709503

Calculate the square root of the right side: 1.431477242

Break this problem into two subproblems by setting 
(t + 0.1019367992) equal to 1.431477242 and -1.431477242.

Subproblem 1

t + 0.1019367992 = 1.431477242 Simplifying t + 0.1019367992 = 1.431477242 Reorder the terms: 0.1019367992 + t = 1.431477242 Solving 0.1019367992 + t = 1.431477242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1019367992' to each side of the equation. 0.1019367992 + -0.1019367992 + t = 1.431477242 + -0.1019367992 Combine like terms: 0.1019367992 + -0.1019367992 = 0.0000000000 0.0000000000 + t = 1.431477242 + -0.1019367992 t = 1.431477242 + -0.1019367992 Combine like terms: 1.431477242 + -0.1019367992 = 1.3295404428 t = 1.3295404428 Simplifying t = 1.3295404428

Subproblem 2

t + 0.1019367992 = -1.431477242 Simplifying t + 0.1019367992 = -1.431477242 Reorder the terms: 0.1019367992 + t = -1.431477242 Solving 0.1019367992 + t = -1.431477242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1019367992' to each side of the equation. 0.1019367992 + -0.1019367992 + t = -1.431477242 + -0.1019367992 Combine like terms: 0.1019367992 + -0.1019367992 = 0.0000000000 0.0000000000 + t = -1.431477242 + -0.1019367992 t = -1.431477242 + -0.1019367992 Combine like terms: -1.431477242 + -0.1019367992 = -1.5334140412 t = -1.5334140412 Simplifying t = -1.5334140412

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.3295404428, -1.5334140412}

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