0=3.9t^2+158t-2300

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Solution for 0=3.9t^2+158t-2300 equation:


Simplifying
0 = 3.9t2 + 158t + -2300

Reorder the terms:
0 = -2300 + 158t + 3.9t2

Solving
0 = -2300 + 158t + 3.9t2

Solving for variable 't'.

Combine like terms: 0 + 2300 = 2300
2300 + -158t + -3.9t2 = -2300 + 158t + 3.9t2 + 2300 + -158t + -3.9t2

Reorder the terms:
2300 + -158t + -3.9t2 = -2300 + 2300 + 158t + -158t + 3.9t2 + -3.9t2

Combine like terms: -2300 + 2300 = 0
2300 + -158t + -3.9t2 = 0 + 158t + -158t + 3.9t2 + -3.9t2
2300 + -158t + -3.9t2 = 158t + -158t + 3.9t2 + -3.9t2

Combine like terms: 158t + -158t = 0
2300 + -158t + -3.9t2 = 0 + 3.9t2 + -3.9t2
2300 + -158t + -3.9t2 = 3.9t2 + -3.9t2

Combine like terms: 3.9t2 + -3.9t2 = 0.0
2300 + -158t + -3.9t2 = 0.0

Begin completing the square.  Divide all terms by
-3.9 the coefficient of the squared term: 

Divide each side by '-3.9'.
-589.7435897 + 40.51282051t + t2 = 0

Move the constant term to the right:

Add '589.7435897' to each side of the equation.
-589.7435897 + 40.51282051t + 589.7435897 + t2 = 0 + 589.7435897

Reorder the terms:
-589.7435897 + 589.7435897 + 40.51282051t + t2 = 0 + 589.7435897

Combine like terms: -589.7435897 + 589.7435897 = 0.0000000
0.0000000 + 40.51282051t + t2 = 0 + 589.7435897
40.51282051t + t2 = 0 + 589.7435897

Combine like terms: 0 + 589.7435897 = 589.7435897
40.51282051t + t2 = 589.7435897

The t term is 40.51282051t.  Take half its coefficient (20.25641026).
Square it (410.3221566) and add it to both sides.

Add '410.3221566' to each side of the equation.
40.51282051t + 410.3221566 + t2 = 589.7435897 + 410.3221566

Reorder the terms:
410.3221566 + 40.51282051t + t2 = 589.7435897 + 410.3221566

Combine like terms: 589.7435897 + 410.3221566 = 1000.0657463
410.3221566 + 40.51282051t + t2 = 1000.0657463

Factor a perfect square on the left side:
(t + 20.25641026)(t + 20.25641026) = 1000.0657463

Calculate the square root of the right side: 31.623816125

Break this problem into two subproblems by setting 
(t + 20.25641026) equal to 31.623816125 and -31.623816125.

Subproblem 1

t + 20.25641026 = 31.623816125 Simplifying t + 20.25641026 = 31.623816125 Reorder the terms: 20.25641026 + t = 31.623816125 Solving 20.25641026 + t = 31.623816125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20.25641026' to each side of the equation. 20.25641026 + -20.25641026 + t = 31.623816125 + -20.25641026 Combine like terms: 20.25641026 + -20.25641026 = 0.00000000 0.00000000 + t = 31.623816125 + -20.25641026 t = 31.623816125 + -20.25641026 Combine like terms: 31.623816125 + -20.25641026 = 11.367405865 t = 11.367405865 Simplifying t = 11.367405865

Subproblem 2

t + 20.25641026 = -31.623816125 Simplifying t + 20.25641026 = -31.623816125 Reorder the terms: 20.25641026 + t = -31.623816125 Solving 20.25641026 + t = -31.623816125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20.25641026' to each side of the equation. 20.25641026 + -20.25641026 + t = -31.623816125 + -20.25641026 Combine like terms: 20.25641026 + -20.25641026 = 0.00000000 0.00000000 + t = -31.623816125 + -20.25641026 t = -31.623816125 + -20.25641026 Combine like terms: -31.623816125 + -20.25641026 = -51.880226385 t = -51.880226385 Simplifying t = -51.880226385

Solution

The solution to the problem is based on the solutions from the subproblems. t = {11.367405865, -51.880226385}

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