0=10-4t-4.9t^2

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Solution for 0=10-4t-4.9t^2 equation:


Simplifying
0 = 10 + -4t + -4.9t2

Solving
0 = 10 + -4t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -10 = -10
-10 + 4t + 4.9t2 = 10 + -4t + -4.9t2 + -10 + 4t + 4.9t2

Reorder the terms:
-10 + 4t + 4.9t2 = 10 + -10 + -4t + 4t + -4.9t2 + 4.9t2

Combine like terms: 10 + -10 = 0
-10 + 4t + 4.9t2 = 0 + -4t + 4t + -4.9t2 + 4.9t2
-10 + 4t + 4.9t2 = -4t + 4t + -4.9t2 + 4.9t2

Combine like terms: -4t + 4t = 0
-10 + 4t + 4.9t2 = 0 + -4.9t2 + 4.9t2
-10 + 4t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-10 + 4t + 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'.
-2.040816327 + 0.8163265306t + t2 = 0

Move the constant term to the right:

Add '2.040816327' to each side of the equation.
-2.040816327 + 0.8163265306t + 2.040816327 + t2 = 0 + 2.040816327

Reorder the terms:
-2.040816327 + 2.040816327 + 0.8163265306t + t2 = 0 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + 0.8163265306t + t2 = 0 + 2.040816327
0.8163265306t + t2 = 0 + 2.040816327

Combine like terms: 0 + 2.040816327 = 2.040816327
0.8163265306t + t2 = 2.040816327

The t term is 0.8163265306t.  Take half its coefficient (0.4081632653).
Square it (0.1665972511) and add it to both sides.

Add '0.1665972511' to each side of the equation.
0.8163265306t + 0.1665972511 + t2 = 2.040816327 + 0.1665972511

Reorder the terms:
0.1665972511 + 0.8163265306t + t2 = 2.040816327 + 0.1665972511

Combine like terms: 2.040816327 + 0.1665972511 = 2.2074135781
0.1665972511 + 0.8163265306t + t2 = 2.2074135781

Factor a perfect square on the left side:
(t + 0.4081632653)(t + 0.4081632653) = 2.2074135781

Calculate the square root of the right side: 1.485736712

Break this problem into two subproblems by setting 
(t + 0.4081632653) equal to 1.485736712 and -1.485736712.

Subproblem 1

t + 0.4081632653 = 1.485736712 Simplifying t + 0.4081632653 = 1.485736712 Reorder the terms: 0.4081632653 + t = 1.485736712 Solving 0.4081632653 + t = 1.485736712 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + t = 1.485736712 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = 1.485736712 + -0.4081632653 t = 1.485736712 + -0.4081632653 Combine like terms: 1.485736712 + -0.4081632653 = 1.0775734467 t = 1.0775734467 Simplifying t = 1.0775734467

Subproblem 2

t + 0.4081632653 = -1.485736712 Simplifying t + 0.4081632653 = -1.485736712 Reorder the terms: 0.4081632653 + t = -1.485736712 Solving 0.4081632653 + t = -1.485736712 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + t = -1.485736712 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = -1.485736712 + -0.4081632653 t = -1.485736712 + -0.4081632653 Combine like terms: -1.485736712 + -0.4081632653 = -1.8938999773 t = -1.8938999773 Simplifying t = -1.8938999773

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.0775734467, -1.8938999773}

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