(7x^2)+91x+66=0

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Solution for (7x^2)+91x+66=0 equation:


Simplifying
(7x2) + 91x + 66 = 0

Reorder the terms:
66 + 91x + (7x2) = 0

Solving
66 + 91x + (7x2) = 0

Solving for variable 'x'.

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

Divide each side by '7'.
9.428571429 + 13x + x2 = 0

Move the constant term to the right:

Add '-9.428571429' to each side of the equation.
9.428571429 + 13x + -9.428571429 + x2 = 0 + -9.428571429

Reorder the terms:
9.428571429 + -9.428571429 + 13x + x2 = 0 + -9.428571429

Combine like terms: 9.428571429 + -9.428571429 = 0.000000000
0.000000000 + 13x + x2 = 0 + -9.428571429
13x + x2 = 0 + -9.428571429

Combine like terms: 0 + -9.428571429 = -9.428571429
13x + x2 = -9.428571429

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -9.428571429 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -9.428571429 + 42.25

Combine like terms: -9.428571429 + 42.25 = 32.821428571
42.25 + 13x + x2 = 32.821428571

Factor a perfect square on the left side:
((x) + 6.5)((x) + 6.5) = 32.821428571

Calculate the square root of the right side: 5.728998915

Break this problem into two subproblems by setting 
((x) + 6.5) equal to 5.728998915 and -5.728998915.

Subproblem 1

(x) + 6.5 = 5.728998915 Simplifying (x) + 6.5 = 5.728998915 x + 6.5 = 5.728998915 Reorder the terms: 6.5 + x = 5.728998915 Solving 6.5 + x = 5.728998915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 5.728998915 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 5.728998915 + -6.5 x = 5.728998915 + -6.5 Combine like terms: 5.728998915 + -6.5 = -0.771001085 x = -0.771001085 Simplifying x = -0.771001085

Subproblem 2

(x) + 6.5 = -5.728998915 Simplifying (x) + 6.5 = -5.728998915 x + 6.5 = -5.728998915 Reorder the terms: 6.5 + x = -5.728998915 Solving 6.5 + x = -5.728998915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -5.728998915 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -5.728998915 + -6.5 x = -5.728998915 + -6.5 Combine like terms: -5.728998915 + -6.5 = -12.228998915 x = -12.228998915 Simplifying x = -12.228998915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.771001085, -12.228998915}

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