5t^2-14t-6=0

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Solution for 5t^2-14t-6=0 equation:


Simplifying
5t2 + -14t + -6 = 0

Reorder the terms:
-6 + -14t + 5t2 = 0

Solving
-6 + -14t + 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'.
-1.2 + -2.8t + t2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.8t + 1.2 + t2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.8t + t2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.8t + t2 = 0 + 1.2
-2.8t + t2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.8t + t2 = 1.2

The t term is -2.8t.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8t + 1.96 + t2 = 1.2 + 1.96

Reorder the terms:
1.96 + -2.8t + t2 = 1.2 + 1.96

Combine like terms: 1.2 + 1.96 = 3.16
1.96 + -2.8t + t2 = 3.16

Factor a perfect square on the left side:
(t + -1.4)(t + -1.4) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(t + -1.4) equal to 1.777638883 and -1.777638883.

Subproblem 1

t + -1.4 = 1.777638883 Simplifying t + -1.4 = 1.777638883 Reorder the terms: -1.4 + t = 1.777638883 Solving -1.4 + t = 1.777638883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + t = 1.777638883 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + t = 1.777638883 + 1.4 t = 1.777638883 + 1.4 Combine like terms: 1.777638883 + 1.4 = 3.177638883 t = 3.177638883 Simplifying t = 3.177638883

Subproblem 2

t + -1.4 = -1.777638883 Simplifying t + -1.4 = -1.777638883 Reorder the terms: -1.4 + t = -1.777638883 Solving -1.4 + t = -1.777638883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + t = -1.777638883 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + t = -1.777638883 + 1.4 t = -1.777638883 + 1.4 Combine like terms: -1.777638883 + 1.4 = -0.377638883 t = -0.377638883 Simplifying t = -0.377638883

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.177638883, -0.377638883}

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