x^2+x-444=0

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Solution for x^2+x-444=0 equation:


Simplifying
x2 + x + -444 = 0

Reorder the terms:
-444 + x + x2 = 0

Solving
-444 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '444' to each side of the equation.
-444 + x + 444 + x2 = 0 + 444

Reorder the terms:
-444 + 444 + x + x2 = 0 + 444

Combine like terms: -444 + 444 = 0
0 + x + x2 = 0 + 444
x + x2 = 0 + 444

Combine like terms: 0 + 444 = 444
x + x2 = 444

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 444 + 0.25

Reorder the terms:
0.25 + x + x2 = 444 + 0.25

Combine like terms: 444 + 0.25 = 444.25
0.25 + x + x2 = 444.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 444.25

Calculate the square root of the right side: 21.077238908

Break this problem into two subproblems by setting 
(x + 0.5) equal to 21.077238908 and -21.077238908.

Subproblem 1

x + 0.5 = 21.077238908 Simplifying x + 0.5 = 21.077238908 Reorder the terms: 0.5 + x = 21.077238908 Solving 0.5 + x = 21.077238908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 21.077238908 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 21.077238908 + -0.5 x = 21.077238908 + -0.5 Combine like terms: 21.077238908 + -0.5 = 20.577238908 x = 20.577238908 Simplifying x = 20.577238908

Subproblem 2

x + 0.5 = -21.077238908 Simplifying x + 0.5 = -21.077238908 Reorder the terms: 0.5 + x = -21.077238908 Solving 0.5 + x = -21.077238908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -21.077238908 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -21.077238908 + -0.5 x = -21.077238908 + -0.5 Combine like terms: -21.077238908 + -0.5 = -21.577238908 x = -21.577238908 Simplifying x = -21.577238908

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.577238908, -21.577238908}

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