x^2+20x-320=0

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Solution for x^2+20x-320=0 equation:


Simplifying
x2 + 20x + -320 = 0

Reorder the terms:
-320 + 20x + x2 = 0

Solving
-320 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + 20x + 320 + x2 = 0 + 320

Reorder the terms:
-320 + 320 + 20x + x2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 20x + x2 = 0 + 320
20x + x2 = 0 + 320

Combine like terms: 0 + 320 = 320
20x + x2 = 320

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 = 320 + 100

Reorder the terms:
100 + 20x + x2 = 320 + 100

Combine like terms: 320 + 100 = 420
100 + 20x + x2 = 420

Factor a perfect square on the left side:
(x + 10)(x + 10) = 420

Calculate the square root of the right side: 20.493901532

Break this problem into two subproblems by setting 
(x + 10) equal to 20.493901532 and -20.493901532.

Subproblem 1

x + 10 = 20.493901532 Simplifying x + 10 = 20.493901532 Reorder the terms: 10 + x = 20.493901532 Solving 10 + x = 20.493901532 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 = 20.493901532 + -10 Combine like terms: 10 + -10 = 0 0 + x = 20.493901532 + -10 x = 20.493901532 + -10 Combine like terms: 20.493901532 + -10 = 10.493901532 x = 10.493901532 Simplifying x = 10.493901532

Subproblem 2

x + 10 = -20.493901532 Simplifying x + 10 = -20.493901532 Reorder the terms: 10 + x = -20.493901532 Solving 10 + x = -20.493901532 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 = -20.493901532 + -10 Combine like terms: 10 + -10 = 0 0 + x = -20.493901532 + -10 x = -20.493901532 + -10 Combine like terms: -20.493901532 + -10 = -30.493901532 x = -30.493901532 Simplifying x = -30.493901532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.493901532, -30.493901532}

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