7x^2-7x-184=0

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Solution for 7x^2-7x-184=0 equation:


Simplifying
7x2 + -7x + -184 = 0

Reorder the terms:
-184 + -7x + 7x2 = 0

Solving
-184 + -7x + 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'.
-26.28571429 + -1x + x2 = 0

Move the constant term to the right:

Add '26.28571429' to each side of the equation.
-26.28571429 + -1x + 26.28571429 + x2 = 0 + 26.28571429

Reorder the terms:
-26.28571429 + 26.28571429 + -1x + x2 = 0 + 26.28571429

Combine like terms: -26.28571429 + 26.28571429 = 0.00000000
0.00000000 + -1x + x2 = 0 + 26.28571429
-1x + x2 = 0 + 26.28571429

Combine like terms: 0 + 26.28571429 = 26.28571429
-1x + x2 = 26.28571429

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 26.28571429 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 26.28571429 + 0.25

Combine like terms: 26.28571429 + 0.25 = 26.53571429
0.25 + -1x + x2 = 26.53571429

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 26.53571429

Calculate the square root of the right side: 5.151282781

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.151282781 and -5.151282781.

Subproblem 1

x + -0.5 = 5.151282781 Simplifying x + -0.5 = 5.151282781 Reorder the terms: -0.5 + x = 5.151282781 Solving -0.5 + x = 5.151282781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.151282781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.151282781 + 0.5 x = 5.151282781 + 0.5 Combine like terms: 5.151282781 + 0.5 = 5.651282781 x = 5.651282781 Simplifying x = 5.651282781

Subproblem 2

x + -0.5 = -5.151282781 Simplifying x + -0.5 = -5.151282781 Reorder the terms: -0.5 + x = -5.151282781 Solving -0.5 + x = -5.151282781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.151282781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.151282781 + 0.5 x = -5.151282781 + 0.5 Combine like terms: -5.151282781 + 0.5 = -4.651282781 x = -4.651282781 Simplifying x = -4.651282781

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.651282781, -4.651282781}

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