0=-4.9t^2+9t+300

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Solution for 0=-4.9t^2+9t+300 equation:


Simplifying
0 = -4.9t2 + 9t + 300

Reorder the terms:
0 = 300 + 9t + -4.9t2

Solving
0 = 300 + 9t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -300 = -300
-300 + -9t + 4.9t2 = 300 + 9t + -4.9t2 + -300 + -9t + 4.9t2

Reorder the terms:
-300 + -9t + 4.9t2 = 300 + -300 + 9t + -9t + -4.9t2 + 4.9t2

Combine like terms: 300 + -300 = 0
-300 + -9t + 4.9t2 = 0 + 9t + -9t + -4.9t2 + 4.9t2
-300 + -9t + 4.9t2 = 9t + -9t + -4.9t2 + 4.9t2

Combine like terms: 9t + -9t = 0
-300 + -9t + 4.9t2 = 0 + -4.9t2 + 4.9t2
-300 + -9t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-300 + -9t + 4.9t2 = 0.0

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

Divide each side by '4.9'.
-61.2244898 + -1.836734694t + t2 = 0

Move the constant term to the right:

Add '61.2244898' to each side of the equation.
-61.2244898 + -1.836734694t + 61.2244898 + t2 = 0 + 61.2244898

Reorder the terms:
-61.2244898 + 61.2244898 + -1.836734694t + t2 = 0 + 61.2244898

Combine like terms: -61.2244898 + 61.2244898 = 0.0000000
0.0000000 + -1.836734694t + t2 = 0 + 61.2244898
-1.836734694t + t2 = 0 + 61.2244898

Combine like terms: 0 + 61.2244898 = 61.2244898
-1.836734694t + t2 = 61.2244898

The t term is -1.836734694t.  Take half its coefficient (-0.918367347).
Square it (0.8433985840) and add it to both sides.

Add '0.8433985840' to each side of the equation.
-1.836734694t + 0.8433985840 + t2 = 61.2244898 + 0.8433985840

Reorder the terms:
0.8433985840 + -1.836734694t + t2 = 61.2244898 + 0.8433985840

Combine like terms: 61.2244898 + 0.8433985840 = 62.067888384
0.8433985840 + -1.836734694t + t2 = 62.067888384

Factor a perfect square on the left side:
(t + -0.918367347)(t + -0.918367347) = 62.067888384

Calculate the square root of the right side: 7.878317611

Break this problem into two subproblems by setting 
(t + -0.918367347) equal to 7.878317611 and -7.878317611.

Subproblem 1

t + -0.918367347 = 7.878317611 Simplifying t + -0.918367347 = 7.878317611 Reorder the terms: -0.918367347 + t = 7.878317611 Solving -0.918367347 + t = 7.878317611 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + t = 7.878317611 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + t = 7.878317611 + 0.918367347 t = 7.878317611 + 0.918367347 Combine like terms: 7.878317611 + 0.918367347 = 8.796684958 t = 8.796684958 Simplifying t = 8.796684958

Subproblem 2

t + -0.918367347 = -7.878317611 Simplifying t + -0.918367347 = -7.878317611 Reorder the terms: -0.918367347 + t = -7.878317611 Solving -0.918367347 + t = -7.878317611 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + t = -7.878317611 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + t = -7.878317611 + 0.918367347 t = -7.878317611 + 0.918367347 Combine like terms: -7.878317611 + 0.918367347 = -6.959950264 t = -6.959950264 Simplifying t = -6.959950264

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.796684958, -6.959950264}

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