x^2+4x-585=0

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Solution for x^2+4x-585=0 equation:


Simplifying
x2 + 4x + -585 = 0

Reorder the terms:
-585 + 4x + x2 = 0

Solving
-585 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '585' to each side of the equation.
-585 + 4x + 585 + x2 = 0 + 585

Reorder the terms:
-585 + 585 + 4x + x2 = 0 + 585

Combine like terms: -585 + 585 = 0
0 + 4x + x2 = 0 + 585
4x + x2 = 0 + 585

Combine like terms: 0 + 585 = 585
4x + x2 = 585

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 585 + 4

Reorder the terms:
4 + 4x + x2 = 585 + 4

Combine like terms: 585 + 4 = 589
4 + 4x + x2 = 589

Factor a perfect square on the left side:
(x + 2)(x + 2) = 589

Calculate the square root of the right side: 24.269322199

Break this problem into two subproblems by setting 
(x + 2) equal to 24.269322199 and -24.269322199.

Subproblem 1

x + 2 = 24.269322199 Simplifying x + 2 = 24.269322199 Reorder the terms: 2 + x = 24.269322199 Solving 2 + x = 24.269322199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 24.269322199 + -2 Combine like terms: 2 + -2 = 0 0 + x = 24.269322199 + -2 x = 24.269322199 + -2 Combine like terms: 24.269322199 + -2 = 22.269322199 x = 22.269322199 Simplifying x = 22.269322199

Subproblem 2

x + 2 = -24.269322199 Simplifying x + 2 = -24.269322199 Reorder the terms: 2 + x = -24.269322199 Solving 2 + x = -24.269322199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -24.269322199 + -2 Combine like terms: 2 + -2 = 0 0 + x = -24.269322199 + -2 x = -24.269322199 + -2 Combine like terms: -24.269322199 + -2 = -26.269322199 x = -26.269322199 Simplifying x = -26.269322199

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.269322199, -26.269322199}

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