-5.3t^2+26.5t=-31.8

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Solution for -5.3t^2+26.5t=-31.8 equation:


Simplifying
-5.3t2 + 26.5t = -31.8

Reorder the terms:
26.5t + -5.3t2 = -31.8

Solving
26.5t + -5.3t2 = -31.8

Solving for variable 't'.

Reorder the terms:
31.8 + 26.5t + -5.3t2 = -31.8 + 31.8

Combine like terms: -31.8 + 31.8 = 0.0
31.8 + 26.5t + -5.3t2 = 0.0

Begin completing the square.  Divide all terms by
-5.3 the coefficient of the squared term: 

Divide each side by '-5.3'.
-6 + -5t + t2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -5t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -5t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5t + t2 = 0 + 6
-5t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-5t + t2 = 6

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = 6 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 6 + 6.25

Combine like terms: 6 + 6.25 = 12.25
6.25 + -5t + t2 = 12.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(t + -2.5) equal to 3.5 and -3.5.

Subproblem 1

t + -2.5 = 3.5 Simplifying t + -2.5 = 3.5 Reorder the terms: -2.5 + t = 3.5 Solving -2.5 + t = 3.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 3.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 3.5 + 2.5 t = 3.5 + 2.5 Combine like terms: 3.5 + 2.5 = 6 t = 6 Simplifying t = 6

Subproblem 2

t + -2.5 = -3.5 Simplifying t + -2.5 = -3.5 Reorder the terms: -2.5 + t = -3.5 Solving -2.5 + t = -3.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -3.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -3.5 + 2.5 t = -3.5 + 2.5 Combine like terms: -3.5 + 2.5 = -1 t = -1 Simplifying t = -1

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6, -1}

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