5t^2-47t=27

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Solution for 5t^2-47t=27 equation:


Simplifying
5t2 + -47t = 27

Reorder the terms:
-47t + 5t2 = 27

Solving
-47t + 5t2 = 27

Solving for variable 't'.

Reorder the terms:
-27 + -47t + 5t2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -47t + 5t2 = 0

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

Divide each side by '5'.
-5.4 + -9.4t + t2 = 0

Move the constant term to the right:

Add '5.4' to each side of the equation.
-5.4 + -9.4t + 5.4 + t2 = 0 + 5.4

Reorder the terms:
-5.4 + 5.4 + -9.4t + t2 = 0 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + -9.4t + t2 = 0 + 5.4
-9.4t + t2 = 0 + 5.4

Combine like terms: 0 + 5.4 = 5.4
-9.4t + t2 = 5.4

The t term is -9.4t.  Take half its coefficient (-4.7).
Square it (22.09) and add it to both sides.

Add '22.09' to each side of the equation.
-9.4t + 22.09 + t2 = 5.4 + 22.09

Reorder the terms:
22.09 + -9.4t + t2 = 5.4 + 22.09

Combine like terms: 5.4 + 22.09 = 27.49
22.09 + -9.4t + t2 = 27.49

Factor a perfect square on the left side:
(t + -4.7)(t + -4.7) = 27.49

Calculate the square root of the right side: 5.243090692

Break this problem into two subproblems by setting 
(t + -4.7) equal to 5.243090692 and -5.243090692.

Subproblem 1

t + -4.7 = 5.243090692 Simplifying t + -4.7 = 5.243090692 Reorder the terms: -4.7 + t = 5.243090692 Solving -4.7 + t = 5.243090692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + t = 5.243090692 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + t = 5.243090692 + 4.7 t = 5.243090692 + 4.7 Combine like terms: 5.243090692 + 4.7 = 9.943090692 t = 9.943090692 Simplifying t = 9.943090692

Subproblem 2

t + -4.7 = -5.243090692 Simplifying t + -4.7 = -5.243090692 Reorder the terms: -4.7 + t = -5.243090692 Solving -4.7 + t = -5.243090692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + t = -5.243090692 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + t = -5.243090692 + 4.7 t = -5.243090692 + 4.7 Combine like terms: -5.243090692 + 4.7 = -0.543090692 t = -0.543090692 Simplifying t = -0.543090692

Solution

The solution to the problem is based on the solutions from the subproblems. t = {9.943090692, -0.543090692}

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