4.9t^2-3.28t-5.89=0

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Solution for 4.9t^2-3.28t-5.89=0 equation:


Simplifying
4.9t2 + -3.28t + -5.89 = 0

Reorder the terms:
-5.89 + -3.28t + 4.9t2 = 0

Solving
-5.89 + -3.28t + 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'.
-1.202040816 + -0.6693877551t + t2 = 0

Move the constant term to the right:

Add '1.202040816' to each side of the equation.
-1.202040816 + -0.6693877551t + 1.202040816 + t2 = 0 + 1.202040816

Reorder the terms:
-1.202040816 + 1.202040816 + -0.6693877551t + t2 = 0 + 1.202040816

Combine like terms: -1.202040816 + 1.202040816 = 0.000000000
0.000000000 + -0.6693877551t + t2 = 0 + 1.202040816
-0.6693877551t + t2 = 0 + 1.202040816

Combine like terms: 0 + 1.202040816 = 1.202040816
-0.6693877551t + t2 = 1.202040816

The t term is -0.6693877551t.  Take half its coefficient (-0.3346938776).
Square it (0.1120199917) and add it to both sides.

Add '0.1120199917' to each side of the equation.
-0.6693877551t + 0.1120199917 + t2 = 1.202040816 + 0.1120199917

Reorder the terms:
0.1120199917 + -0.6693877551t + t2 = 1.202040816 + 0.1120199917

Combine like terms: 1.202040816 + 0.1120199917 = 1.3140608077
0.1120199917 + -0.6693877551t + t2 = 1.3140608077

Factor a perfect square on the left side:
(t + -0.3346938776)(t + -0.3346938776) = 1.3140608077

Calculate the square root of the right side: 1.146324914

Break this problem into two subproblems by setting 
(t + -0.3346938776) equal to 1.146324914 and -1.146324914.

Subproblem 1

t + -0.3346938776 = 1.146324914 Simplifying t + -0.3346938776 = 1.146324914 Reorder the terms: -0.3346938776 + t = 1.146324914 Solving -0.3346938776 + t = 1.146324914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3346938776' to each side of the equation. -0.3346938776 + 0.3346938776 + t = 1.146324914 + 0.3346938776 Combine like terms: -0.3346938776 + 0.3346938776 = 0.0000000000 0.0000000000 + t = 1.146324914 + 0.3346938776 t = 1.146324914 + 0.3346938776 Combine like terms: 1.146324914 + 0.3346938776 = 1.4810187916 t = 1.4810187916 Simplifying t = 1.4810187916

Subproblem 2

t + -0.3346938776 = -1.146324914 Simplifying t + -0.3346938776 = -1.146324914 Reorder the terms: -0.3346938776 + t = -1.146324914 Solving -0.3346938776 + t = -1.146324914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3346938776' to each side of the equation. -0.3346938776 + 0.3346938776 + t = -1.146324914 + 0.3346938776 Combine like terms: -0.3346938776 + 0.3346938776 = 0.0000000000 0.0000000000 + t = -1.146324914 + 0.3346938776 t = -1.146324914 + 0.3346938776 Combine like terms: -1.146324914 + 0.3346938776 = -0.8116310364 t = -0.8116310364 Simplifying t = -0.8116310364

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.4810187916, -0.8116310364}

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