3x^2-84x-91=0

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Solution for 3x^2-84x-91=0 equation:


Simplifying
3x2 + -84x + -91 = 0

Reorder the terms:
-91 + -84x + 3x2 = 0

Solving
-91 + -84x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-30.33333333 + -28x + x2 = 0

Move the constant term to the right:

Add '30.33333333' to each side of the equation.
-30.33333333 + -28x + 30.33333333 + x2 = 0 + 30.33333333

Reorder the terms:
-30.33333333 + 30.33333333 + -28x + x2 = 0 + 30.33333333

Combine like terms: -30.33333333 + 30.33333333 = 0.00000000
0.00000000 + -28x + x2 = 0 + 30.33333333
-28x + x2 = 0 + 30.33333333

Combine like terms: 0 + 30.33333333 = 30.33333333
-28x + x2 = 30.33333333

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = 30.33333333 + 196

Reorder the terms:
196 + -28x + x2 = 30.33333333 + 196

Combine like terms: 30.33333333 + 196 = 226.33333333
196 + -28x + x2 = 226.33333333

Factor a perfect square on the left side:
(x + -14)(x + -14) = 226.33333333

Calculate the square root of the right side: 15.044378795

Break this problem into two subproblems by setting 
(x + -14) equal to 15.044378795 and -15.044378795.

Subproblem 1

x + -14 = 15.044378795 Simplifying x + -14 = 15.044378795 Reorder the terms: -14 + x = 15.044378795 Solving -14 + x = 15.044378795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 15.044378795 + 14 Combine like terms: -14 + 14 = 0 0 + x = 15.044378795 + 14 x = 15.044378795 + 14 Combine like terms: 15.044378795 + 14 = 29.044378795 x = 29.044378795 Simplifying x = 29.044378795

Subproblem 2

x + -14 = -15.044378795 Simplifying x + -14 = -15.044378795 Reorder the terms: -14 + x = -15.044378795 Solving -14 + x = -15.044378795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -15.044378795 + 14 Combine like terms: -14 + 14 = 0 0 + x = -15.044378795 + 14 x = -15.044378795 + 14 Combine like terms: -15.044378795 + 14 = -1.044378795 x = -1.044378795 Simplifying x = -1.044378795

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.044378795, -1.044378795}

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