7-6t-5t^2=0

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Solution for 7-6t-5t^2=0 equation:


Simplifying
7 + -6t + -5t2 = 0

Solving
7 + -6t + -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'.
-1.4 + 1.2t + t2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 1.2t + 1.4 + t2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 1.2t + t2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 1.2t + t2 = 0 + 1.4
1.2t + t2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
1.2t + t2 = 1.4

The t term is 1.2t.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2t + 0.36 + t2 = 1.4 + 0.36

Reorder the terms:
0.36 + 1.2t + t2 = 1.4 + 0.36

Combine like terms: 1.4 + 0.36 = 1.76
0.36 + 1.2t + t2 = 1.76

Factor a perfect square on the left side:
(t + 0.6)(t + 0.6) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(t + 0.6) equal to 1.326649916 and -1.326649916.

Subproblem 1

t + 0.6 = 1.326649916 Simplifying t + 0.6 = 1.326649916 Reorder the terms: 0.6 + t = 1.326649916 Solving 0.6 + t = 1.326649916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = 1.326649916 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = 1.326649916 + -0.6 t = 1.326649916 + -0.6 Combine like terms: 1.326649916 + -0.6 = 0.726649916 t = 0.726649916 Simplifying t = 0.726649916

Subproblem 2

t + 0.6 = -1.326649916 Simplifying t + 0.6 = -1.326649916 Reorder the terms: 0.6 + t = -1.326649916 Solving 0.6 + t = -1.326649916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = -1.326649916 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = -1.326649916 + -0.6 t = -1.326649916 + -0.6 Combine like terms: -1.326649916 + -0.6 = -1.926649916 t = -1.926649916 Simplifying t = -1.926649916

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.726649916, -1.926649916}

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