x^2+6x-1890=0

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Solution for x^2+6x-1890=0 equation:


Simplifying
x2 + 6x + -1890 = 0

Reorder the terms:
-1890 + 6x + x2 = 0

Solving
-1890 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1890' to each side of the equation.
-1890 + 6x + 1890 + x2 = 0 + 1890

Reorder the terms:
-1890 + 1890 + 6x + x2 = 0 + 1890

Combine like terms: -1890 + 1890 = 0
0 + 6x + x2 = 0 + 1890
6x + x2 = 0 + 1890

Combine like terms: 0 + 1890 = 1890
6x + x2 = 1890

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1890 + 9

Reorder the terms:
9 + 6x + x2 = 1890 + 9

Combine like terms: 1890 + 9 = 1899
9 + 6x + x2 = 1899

Factor a perfect square on the left side:
(x + 3)(x + 3) = 1899

Calculate the square root of the right side: 43.577517139

Break this problem into two subproblems by setting 
(x + 3) equal to 43.577517139 and -43.577517139.

Subproblem 1

x + 3 = 43.577517139 Simplifying x + 3 = 43.577517139 Reorder the terms: 3 + x = 43.577517139 Solving 3 + x = 43.577517139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 43.577517139 + -3 Combine like terms: 3 + -3 = 0 0 + x = 43.577517139 + -3 x = 43.577517139 + -3 Combine like terms: 43.577517139 + -3 = 40.577517139 x = 40.577517139 Simplifying x = 40.577517139

Subproblem 2

x + 3 = -43.577517139 Simplifying x + 3 = -43.577517139 Reorder the terms: 3 + x = -43.577517139 Solving 3 + x = -43.577517139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -43.577517139 + -3 Combine like terms: 3 + -3 = 0 0 + x = -43.577517139 + -3 x = -43.577517139 + -3 Combine like terms: -43.577517139 + -3 = -46.577517139 x = -46.577517139 Simplifying x = -46.577517139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.577517139, -46.577517139}

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