-5t^2+73t-47=0

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Solution for -5t^2+73t-47=0 equation:


Simplifying
-5t2 + 73t + -47 = 0

Reorder the terms:
-47 + 73t + -5t2 = 0

Solving
-47 + 73t + -5t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
9.4 + -14.6t + t2 = 0

Move the constant term to the right:

Add '-9.4' to each side of the equation.
9.4 + -14.6t + -9.4 + t2 = 0 + -9.4

Reorder the terms:
9.4 + -9.4 + -14.6t + t2 = 0 + -9.4

Combine like terms: 9.4 + -9.4 = 0.0
0.0 + -14.6t + t2 = 0 + -9.4
-14.6t + t2 = 0 + -9.4

Combine like terms: 0 + -9.4 = -9.4
-14.6t + t2 = -9.4

The t term is -14.6t.  Take half its coefficient (-7.3).
Square it (53.29) and add it to both sides.

Add '53.29' to each side of the equation.
-14.6t + 53.29 + t2 = -9.4 + 53.29

Reorder the terms:
53.29 + -14.6t + t2 = -9.4 + 53.29

Combine like terms: -9.4 + 53.29 = 43.89
53.29 + -14.6t + t2 = 43.89

Factor a perfect square on the left side:
(t + -7.3)(t + -7.3) = 43.89

Calculate the square root of the right side: 6.62495283

Break this problem into two subproblems by setting 
(t + -7.3) equal to 6.62495283 and -6.62495283.

Subproblem 1

t + -7.3 = 6.62495283 Simplifying t + -7.3 = 6.62495283 Reorder the terms: -7.3 + t = 6.62495283 Solving -7.3 + t = 6.62495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.3' to each side of the equation. -7.3 + 7.3 + t = 6.62495283 + 7.3 Combine like terms: -7.3 + 7.3 = 0.0 0.0 + t = 6.62495283 + 7.3 t = 6.62495283 + 7.3 Combine like terms: 6.62495283 + 7.3 = 13.92495283 t = 13.92495283 Simplifying t = 13.92495283

Subproblem 2

t + -7.3 = -6.62495283 Simplifying t + -7.3 = -6.62495283 Reorder the terms: -7.3 + t = -6.62495283 Solving -7.3 + t = -6.62495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.3' to each side of the equation. -7.3 + 7.3 + t = -6.62495283 + 7.3 Combine like terms: -7.3 + 7.3 = 0.0 0.0 + t = -6.62495283 + 7.3 t = -6.62495283 + 7.3 Combine like terms: -6.62495283 + 7.3 = 0.67504717 t = 0.67504717 Simplifying t = 0.67504717

Solution

The solution to the problem is based on the solutions from the subproblems. t = {13.92495283, 0.67504717}

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