-4.9t^2+1.5t+3.4=0

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Solution for -4.9t^2+1.5t+3.4=0 equation:


Simplifying
-4.9t2 + 1.5t + 3.4 = 0

Reorder the terms:
3.4 + 1.5t + -4.9t2 = 0

Solving
3.4 + 1.5t + -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'.
-0.693877551 + -0.306122449t + t2 = 0

Move the constant term to the right:

Add '0.693877551' to each side of the equation.
-0.693877551 + -0.306122449t + 0.693877551 + t2 = 0 + 0.693877551

Reorder the terms:
-0.693877551 + 0.693877551 + -0.306122449t + t2 = 0 + 0.693877551

Combine like terms: -0.693877551 + 0.693877551 = 0.000000000
0.000000000 + -0.306122449t + t2 = 0 + 0.693877551
-0.306122449t + t2 = 0 + 0.693877551

Combine like terms: 0 + 0.693877551 = 0.693877551
-0.306122449t + t2 = 0.693877551

The t term is -0.306122449t.  Take half its coefficient (-0.1530612245).
Square it (0.02342773845) and add it to both sides.

Add '0.02342773845' to each side of the equation.
-0.306122449t + 0.02342773845 + t2 = 0.693877551 + 0.02342773845

Reorder the terms:
0.02342773845 + -0.306122449t + t2 = 0.693877551 + 0.02342773845

Combine like terms: 0.693877551 + 0.02342773845 = 0.71730528945
0.02342773845 + -0.306122449t + t2 = 0.71730528945

Factor a perfect square on the left side:
(t + -0.1530612245)(t + -0.1530612245) = 0.71730528945

Calculate the square root of the right side: 0.846938776

Break this problem into two subproblems by setting 
(t + -0.1530612245) equal to 0.846938776 and -0.846938776.

Subproblem 1

t + -0.1530612245 = 0.846938776 Simplifying t + -0.1530612245 = 0.846938776 Reorder the terms: -0.1530612245 + t = 0.846938776 Solving -0.1530612245 + t = 0.846938776 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + t = 0.846938776 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = 0.846938776 + 0.1530612245 t = 0.846938776 + 0.1530612245 Combine like terms: 0.846938776 + 0.1530612245 = 1.0000000005 t = 1.0000000005 Simplifying t = 1.0000000005

Subproblem 2

t + -0.1530612245 = -0.846938776 Simplifying t + -0.1530612245 = -0.846938776 Reorder the terms: -0.1530612245 + t = -0.846938776 Solving -0.1530612245 + t = -0.846938776 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + t = -0.846938776 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = -0.846938776 + 0.1530612245 t = -0.846938776 + 0.1530612245 Combine like terms: -0.846938776 + 0.1530612245 = -0.6938775515 t = -0.6938775515 Simplifying t = -0.6938775515

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.0000000005, -0.6938775515}

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