x^2+x-792=0

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Solution for x^2+x-792=0 equation:


Simplifying
x2 + x + -792 = 0

Reorder the terms:
-792 + x + x2 = 0

Solving
-792 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '792' to each side of the equation.
-792 + x + 792 + x2 = 0 + 792

Reorder the terms:
-792 + 792 + x + x2 = 0 + 792

Combine like terms: -792 + 792 = 0
0 + x + x2 = 0 + 792
x + x2 = 0 + 792

Combine like terms: 0 + 792 = 792
x + x2 = 792

The x term is x.  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.
x + 0.25 + x2 = 792 + 0.25

Reorder the terms:
0.25 + x + x2 = 792 + 0.25

Combine like terms: 792 + 0.25 = 792.25
0.25 + x + x2 = 792.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 792.25

Calculate the square root of the right side: 28.14693589

Break this problem into two subproblems by setting 
(x + 0.5) equal to 28.14693589 and -28.14693589.

Subproblem 1

x + 0.5 = 28.14693589 Simplifying x + 0.5 = 28.14693589 Reorder the terms: 0.5 + x = 28.14693589 Solving 0.5 + x = 28.14693589 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 = 28.14693589 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 28.14693589 + -0.5 x = 28.14693589 + -0.5 Combine like terms: 28.14693589 + -0.5 = 27.64693589 x = 27.64693589 Simplifying x = 27.64693589

Subproblem 2

x + 0.5 = -28.14693589 Simplifying x + 0.5 = -28.14693589 Reorder the terms: 0.5 + x = -28.14693589 Solving 0.5 + x = -28.14693589 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 = -28.14693589 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -28.14693589 + -0.5 x = -28.14693589 + -0.5 Combine like terms: -28.14693589 + -0.5 = -28.64693589 x = -28.64693589 Simplifying x = -28.64693589

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.64693589, -28.64693589}

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