x^2+20x-234=0

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Solution for x^2+20x-234=0 equation:


Simplifying
x2 + 20x + -234 = 0

Reorder the terms:
-234 + 20x + x2 = 0

Solving
-234 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '234' to each side of the equation.
-234 + 20x + 234 + x2 = 0 + 234

Reorder the terms:
-234 + 234 + 20x + x2 = 0 + 234

Combine like terms: -234 + 234 = 0
0 + 20x + x2 = 0 + 234
20x + x2 = 0 + 234

Combine like terms: 0 + 234 = 234
20x + x2 = 234

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 234 + 100

Reorder the terms:
100 + 20x + x2 = 234 + 100

Combine like terms: 234 + 100 = 334
100 + 20x + x2 = 334

Factor a perfect square on the left side:
(x + 10)(x + 10) = 334

Calculate the square root of the right side: 18.275666882

Break this problem into two subproblems by setting 
(x + 10) equal to 18.275666882 and -18.275666882.

Subproblem 1

x + 10 = 18.275666882 Simplifying x + 10 = 18.275666882 Reorder the terms: 10 + x = 18.275666882 Solving 10 + x = 18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 18.275666882 + -10 Combine like terms: 10 + -10 = 0 0 + x = 18.275666882 + -10 x = 18.275666882 + -10 Combine like terms: 18.275666882 + -10 = 8.275666882 x = 8.275666882 Simplifying x = 8.275666882

Subproblem 2

x + 10 = -18.275666882 Simplifying x + 10 = -18.275666882 Reorder the terms: 10 + x = -18.275666882 Solving 10 + x = -18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -18.275666882 + -10 Combine like terms: 10 + -10 = 0 0 + x = -18.275666882 + -10 x = -18.275666882 + -10 Combine like terms: -18.275666882 + -10 = -28.275666882 x = -28.275666882 Simplifying x = -28.275666882

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.275666882, -28.275666882}

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