7=-.333t^2+7.333t

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Solution for 7=-.333t^2+7.333t equation:


Simplifying
7 = -0.333t2 + 7.333t

Reorder the terms:
7 = 7.333t + -0.333t2

Solving
7 = 7.333t + -0.333t2

Solving for variable 't'.

Reorder the terms:
7 + -7.333t + 0.333t2 = 7.333t + -7.333t + -0.333t2 + 0.333t2

Combine like terms: 7.333t + -7.333t = 0.000
7 + -7.333t + 0.333t2 = 0.000 + -0.333t2 + 0.333t2
7 + -7.333t + 0.333t2 = -0.333t2 + 0.333t2

Combine like terms: -0.333t2 + 0.333t2 = 0.000
7 + -7.333t + 0.333t2 = 0.000

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

Divide each side by '0.333'.
21.02102102 + -22.02102102t + t2 = 0

Move the constant term to the right:

Add '-21.02102102' to each side of the equation.
21.02102102 + -22.02102102t + -21.02102102 + t2 = 0 + -21.02102102

Reorder the terms:
21.02102102 + -21.02102102 + -22.02102102t + t2 = 0 + -21.02102102

Combine like terms: 21.02102102 + -21.02102102 = 0.00000000
0.00000000 + -22.02102102t + t2 = 0 + -21.02102102
-22.02102102t + t2 = 0 + -21.02102102

Combine like terms: 0 + -21.02102102 = -21.02102102
-22.02102102t + t2 = -21.02102102

The t term is -22.02102102t.  Take half its coefficient (-11.01051051).
Square it (121.2313417) and add it to both sides.

Add '121.2313417' to each side of the equation.
-22.02102102t + 121.2313417 + t2 = -21.02102102 + 121.2313417

Reorder the terms:
121.2313417 + -22.02102102t + t2 = -21.02102102 + 121.2313417

Combine like terms: -21.02102102 + 121.2313417 = 100.21032068
121.2313417 + -22.02102102t + t2 = 100.21032068

Factor a perfect square on the left side:
(t + -11.01051051)(t + -11.01051051) = 100.21032068

Calculate the square root of the right side: 10.01051051

Break this problem into two subproblems by setting 
(t + -11.01051051) equal to 10.01051051 and -10.01051051.

Subproblem 1

t + -11.01051051 = 10.01051051 Simplifying t + -11.01051051 = 10.01051051 Reorder the terms: -11.01051051 + t = 10.01051051 Solving -11.01051051 + t = 10.01051051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.01051051' to each side of the equation. -11.01051051 + 11.01051051 + t = 10.01051051 + 11.01051051 Combine like terms: -11.01051051 + 11.01051051 = 0.00000000 0.00000000 + t = 10.01051051 + 11.01051051 t = 10.01051051 + 11.01051051 Combine like terms: 10.01051051 + 11.01051051 = 21.02102102 t = 21.02102102 Simplifying t = 21.02102102

Subproblem 2

t + -11.01051051 = -10.01051051 Simplifying t + -11.01051051 = -10.01051051 Reorder the terms: -11.01051051 + t = -10.01051051 Solving -11.01051051 + t = -10.01051051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.01051051' to each side of the equation. -11.01051051 + 11.01051051 + t = -10.01051051 + 11.01051051 Combine like terms: -11.01051051 + 11.01051051 = 0.00000000 0.00000000 + t = -10.01051051 + 11.01051051 t = -10.01051051 + 11.01051051 Combine like terms: -10.01051051 + 11.01051051 = 1 t = 1 Simplifying t = 1

Solution

The solution to the problem is based on the solutions from the subproblems. t = {21.02102102, 1}

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