-8t^2-7t+65=0

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Solution for -8t^2-7t+65=0 equation:


Simplifying
-8t2 + -7t + 65 = 0

Reorder the terms:
65 + -7t + -8t2 = 0

Solving
65 + -7t + -8t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-8.125 + 0.875t + t2 = 0

Move the constant term to the right:

Add '8.125' to each side of the equation.
-8.125 + 0.875t + 8.125 + t2 = 0 + 8.125

Reorder the terms:
-8.125 + 8.125 + 0.875t + t2 = 0 + 8.125

Combine like terms: -8.125 + 8.125 = 0.000
0.000 + 0.875t + t2 = 0 + 8.125
0.875t + t2 = 0 + 8.125

Combine like terms: 0 + 8.125 = 8.125
0.875t + t2 = 8.125

The t term is 0.875t.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875t + 0.19140625 + t2 = 8.125 + 0.19140625

Reorder the terms:
0.19140625 + 0.875t + t2 = 8.125 + 0.19140625

Combine like terms: 8.125 + 0.19140625 = 8.31640625
0.19140625 + 0.875t + t2 = 8.31640625

Factor a perfect square on the left side:
(t + 0.4375)(t + 0.4375) = 8.31640625

Calculate the square root of the right side: 2.883817999

Break this problem into two subproblems by setting 
(t + 0.4375) equal to 2.883817999 and -2.883817999.

Subproblem 1

t + 0.4375 = 2.883817999 Simplifying t + 0.4375 = 2.883817999 Reorder the terms: 0.4375 + t = 2.883817999 Solving 0.4375 + t = 2.883817999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + t = 2.883817999 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = 2.883817999 + -0.4375 t = 2.883817999 + -0.4375 Combine like terms: 2.883817999 + -0.4375 = 2.446317999 t = 2.446317999 Simplifying t = 2.446317999

Subproblem 2

t + 0.4375 = -2.883817999 Simplifying t + 0.4375 = -2.883817999 Reorder the terms: 0.4375 + t = -2.883817999 Solving 0.4375 + t = -2.883817999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + t = -2.883817999 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = -2.883817999 + -0.4375 t = -2.883817999 + -0.4375 Combine like terms: -2.883817999 + -0.4375 = -3.321317999 t = -3.321317999 Simplifying t = -3.321317999

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.446317999, -3.321317999}

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