5t^2-12t-14=0

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Solution for 5t^2-12t-14=0 equation:


Simplifying
5t2 + -12t + -14 = 0

Reorder the terms:
-14 + -12t + 5t2 = 0

Solving
-14 + -12t + 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'.
-2.8 + -2.4t + t2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -2.4t + 2.8 + t2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -2.4t + t2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -2.4t + t2 = 0 + 2.8
-2.4t + t2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-2.4t + t2 = 2.8

The t term is -2.4t.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4t + 1.44 + t2 = 2.8 + 1.44

Reorder the terms:
1.44 + -2.4t + t2 = 2.8 + 1.44

Combine like terms: 2.8 + 1.44 = 4.24
1.44 + -2.4t + t2 = 4.24

Factor a perfect square on the left side:
(t + -1.2)(t + -1.2) = 4.24

Calculate the square root of the right side: 2.059126028

Break this problem into two subproblems by setting 
(t + -1.2) equal to 2.059126028 and -2.059126028.

Subproblem 1

t + -1.2 = 2.059126028 Simplifying t + -1.2 = 2.059126028 Reorder the terms: -1.2 + t = 2.059126028 Solving -1.2 + t = 2.059126028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = 2.059126028 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 2.059126028 + 1.2 t = 2.059126028 + 1.2 Combine like terms: 2.059126028 + 1.2 = 3.259126028 t = 3.259126028 Simplifying t = 3.259126028

Subproblem 2

t + -1.2 = -2.059126028 Simplifying t + -1.2 = -2.059126028 Reorder the terms: -1.2 + t = -2.059126028 Solving -1.2 + t = -2.059126028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = -2.059126028 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -2.059126028 + 1.2 t = -2.059126028 + 1.2 Combine like terms: -2.059126028 + 1.2 = -0.859126028 t = -0.859126028 Simplifying t = -0.859126028

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.259126028, -0.859126028}

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