0=-4.9t^2+11.5t-2

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Solution for 0=-4.9t^2+11.5t-2 equation:


Simplifying
0 = -4.9t2 + 11.5t + -2

Reorder the terms:
0 = -2 + 11.5t + -4.9t2

Solving
0 = -2 + 11.5t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + 2 = 2
2 + -11.5t + 4.9t2 = -2 + 11.5t + -4.9t2 + 2 + -11.5t + 4.9t2

Reorder the terms:
2 + -11.5t + 4.9t2 = -2 + 2 + 11.5t + -11.5t + -4.9t2 + 4.9t2

Combine like terms: -2 + 2 = 0
2 + -11.5t + 4.9t2 = 0 + 11.5t + -11.5t + -4.9t2 + 4.9t2
2 + -11.5t + 4.9t2 = 11.5t + -11.5t + -4.9t2 + 4.9t2

Combine like terms: 11.5t + -11.5t = 0.0
2 + -11.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
2 + -11.5t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
2 + -11.5t + 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'.
0.4081632653 + -2.346938776t + t2 = 0

Move the constant term to the right:

Add '-0.4081632653' to each side of the equation.
0.4081632653 + -2.346938776t + -0.4081632653 + t2 = 0 + -0.4081632653

Reorder the terms:
0.4081632653 + -0.4081632653 + -2.346938776t + t2 = 0 + -0.4081632653

Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000
0.0000000000 + -2.346938776t + t2 = 0 + -0.4081632653
-2.346938776t + t2 = 0 + -0.4081632653

Combine like terms: 0 + -0.4081632653 = -0.4081632653
-2.346938776t + t2 = -0.4081632653

The t term is -2.346938776t.  Take half its coefficient (-1.173469388).
Square it (1.377030405) and add it to both sides.

Add '1.377030405' to each side of the equation.
-2.346938776t + 1.377030405 + t2 = -0.4081632653 + 1.377030405

Reorder the terms:
1.377030405 + -2.346938776t + t2 = -0.4081632653 + 1.377030405

Combine like terms: -0.4081632653 + 1.377030405 = 0.9688671397
1.377030405 + -2.346938776t + t2 = 0.9688671397

Factor a perfect square on the left side:
(t + -1.173469388)(t + -1.173469388) = 0.9688671397

Calculate the square root of the right side: 0.984310489

Break this problem into two subproblems by setting 
(t + -1.173469388) equal to 0.984310489 and -0.984310489.

Subproblem 1

t + -1.173469388 = 0.984310489 Simplifying t + -1.173469388 = 0.984310489 Reorder the terms: -1.173469388 + t = 0.984310489 Solving -1.173469388 + t = 0.984310489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.173469388' to each side of the equation. -1.173469388 + 1.173469388 + t = 0.984310489 + 1.173469388 Combine like terms: -1.173469388 + 1.173469388 = 0.000000000 0.000000000 + t = 0.984310489 + 1.173469388 t = 0.984310489 + 1.173469388 Combine like terms: 0.984310489 + 1.173469388 = 2.157779877 t = 2.157779877 Simplifying t = 2.157779877

Subproblem 2

t + -1.173469388 = -0.984310489 Simplifying t + -1.173469388 = -0.984310489 Reorder the terms: -1.173469388 + t = -0.984310489 Solving -1.173469388 + t = -0.984310489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.173469388' to each side of the equation. -1.173469388 + 1.173469388 + t = -0.984310489 + 1.173469388 Combine like terms: -1.173469388 + 1.173469388 = 0.000000000 0.000000000 + t = -0.984310489 + 1.173469388 t = -0.984310489 + 1.173469388 Combine like terms: -0.984310489 + 1.173469388 = 0.189158899 t = 0.189158899 Simplifying t = 0.189158899

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.157779877, 0.189158899}

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