x^2+20x-1800=0

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Solution for x^2+20x-1800=0 equation:


Simplifying
x2 + 20x + -1800 = 0

Reorder the terms:
-1800 + 20x + x2 = 0

Solving
-1800 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1800' to each side of the equation.
-1800 + 20x + 1800 + x2 = 0 + 1800

Reorder the terms:
-1800 + 1800 + 20x + x2 = 0 + 1800

Combine like terms: -1800 + 1800 = 0
0 + 20x + x2 = 0 + 1800
20x + x2 = 0 + 1800

Combine like terms: 0 + 1800 = 1800
20x + x2 = 1800

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 = 1800 + 100

Reorder the terms:
100 + 20x + x2 = 1800 + 100

Combine like terms: 1800 + 100 = 1900
100 + 20x + x2 = 1900

Factor a perfect square on the left side:
(x + 10)(x + 10) = 1900

Calculate the square root of the right side: 43.588989435

Break this problem into two subproblems by setting 
(x + 10) equal to 43.588989435 and -43.588989435.

Subproblem 1

x + 10 = 43.588989435 Simplifying x + 10 = 43.588989435 Reorder the terms: 10 + x = 43.588989435 Solving 10 + x = 43.588989435 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 = 43.588989435 + -10 Combine like terms: 10 + -10 = 0 0 + x = 43.588989435 + -10 x = 43.588989435 + -10 Combine like terms: 43.588989435 + -10 = 33.588989435 x = 33.588989435 Simplifying x = 33.588989435

Subproblem 2

x + 10 = -43.588989435 Simplifying x + 10 = -43.588989435 Reorder the terms: 10 + x = -43.588989435 Solving 10 + x = -43.588989435 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 = -43.588989435 + -10 Combine like terms: 10 + -10 = 0 0 + x = -43.588989435 + -10 x = -43.588989435 + -10 Combine like terms: -43.588989435 + -10 = -53.588989435 x = -53.588989435 Simplifying x = -53.588989435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {33.588989435, -53.588989435}

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