-4.9t^2+34t+289=288.09

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Solution for -4.9t^2+34t+289=288.09 equation:


Simplifying
-4.9t2 + 34t + 289 = 288.09

Reorder the terms:
289 + 34t + -4.9t2 = 288.09

Solving
289 + 34t + -4.9t2 = 288.09

Solving for variable 't'.

Reorder the terms:
289 + -288.09 + 34t + -4.9t2 = 288.09 + -288.09

Combine like terms: 289 + -288.09 = 0.91
0.91 + 34t + -4.9t2 = 288.09 + -288.09

Combine like terms: 288.09 + -288.09 = 0.00
0.91 + 34t + -4.9t2 = 0.00

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-0.1857142857 + -6.93877551t + t2 = 0.0

Move the constant term to the right:

Add '0.1857142857' to each side of the equation.
-0.1857142857 + -6.93877551t + 0.1857142857 + t2 = 0.0 + 0.1857142857

Reorder the terms:
-0.1857142857 + 0.1857142857 + -6.93877551t + t2 = 0.0 + 0.1857142857

Combine like terms: -0.1857142857 + 0.1857142857 = 0.0000000000
0.0000000000 + -6.93877551t + t2 = 0.0 + 0.1857142857
-6.93877551t + t2 = 0.0 + 0.1857142857

Combine like terms: 0.0 + 0.1857142857 = 0.1857142857
-6.93877551t + t2 = 0.1857142857

The t term is -6.93877551t.  Take half its coefficient (-3.469387755).
Square it (12.03665139) and add it to both sides.

Add '12.03665139' to each side of the equation.
-6.93877551t + 12.03665139 + t2 = 0.1857142857 + 12.03665139

Reorder the terms:
12.03665139 + -6.93877551t + t2 = 0.1857142857 + 12.03665139

Combine like terms: 0.1857142857 + 12.03665139 = 12.2223656757
12.03665139 + -6.93877551t + t2 = 12.2223656757

Factor a perfect square on the left side:
(t + -3.469387755)(t + -3.469387755) = 12.2223656757

Calculate the square root of the right side: 3.49605001

Break this problem into two subproblems by setting 
(t + -3.469387755) equal to 3.49605001 and -3.49605001.

Subproblem 1

t + -3.469387755 = 3.49605001 Simplifying t + -3.469387755 = 3.49605001 Reorder the terms: -3.469387755 + t = 3.49605001 Solving -3.469387755 + t = 3.49605001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.469387755' to each side of the equation. -3.469387755 + 3.469387755 + t = 3.49605001 + 3.469387755 Combine like terms: -3.469387755 + 3.469387755 = 0.000000000 0.000000000 + t = 3.49605001 + 3.469387755 t = 3.49605001 + 3.469387755 Combine like terms: 3.49605001 + 3.469387755 = 6.965437765 t = 6.965437765 Simplifying t = 6.965437765

Subproblem 2

t + -3.469387755 = -3.49605001 Simplifying t + -3.469387755 = -3.49605001 Reorder the terms: -3.469387755 + t = -3.49605001 Solving -3.469387755 + t = -3.49605001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.469387755' to each side of the equation. -3.469387755 + 3.469387755 + t = -3.49605001 + 3.469387755 Combine like terms: -3.469387755 + 3.469387755 = 0.000000000 0.000000000 + t = -3.49605001 + 3.469387755 t = -3.49605001 + 3.469387755 Combine like terms: -3.49605001 + 3.469387755 = -0.026662255 t = -0.026662255 Simplifying t = -0.026662255

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.965437765, -0.026662255}

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