x^2+46x+518=0

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Solution for x^2+46x+518=0 equation:


Simplifying
x2 + 46x + 518 = 0

Reorder the terms:
518 + 46x + x2 = 0

Solving
518 + 46x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-518' to each side of the equation.
518 + 46x + -518 + x2 = 0 + -518

Reorder the terms:
518 + -518 + 46x + x2 = 0 + -518

Combine like terms: 518 + -518 = 0
0 + 46x + x2 = 0 + -518
46x + x2 = 0 + -518

Combine like terms: 0 + -518 = -518
46x + x2 = -518

The x term is 46x.  Take half its coefficient (23).
Square it (529) and add it to both sides.

Add '529' to each side of the equation.
46x + 529 + x2 = -518 + 529

Reorder the terms:
529 + 46x + x2 = -518 + 529

Combine like terms: -518 + 529 = 11
529 + 46x + x2 = 11

Factor a perfect square on the left side:
(x + 23)(x + 23) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 23) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + 23 = 3.31662479 Simplifying x + 23 = 3.31662479 Reorder the terms: 23 + x = 3.31662479 Solving 23 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 3.31662479 + -23 Combine like terms: 23 + -23 = 0 0 + x = 3.31662479 + -23 x = 3.31662479 + -23 Combine like terms: 3.31662479 + -23 = -19.68337521 x = -19.68337521 Simplifying x = -19.68337521

Subproblem 2

x + 23 = -3.31662479 Simplifying x + 23 = -3.31662479 Reorder the terms: 23 + x = -3.31662479 Solving 23 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -3.31662479 + -23 Combine like terms: 23 + -23 = 0 0 + x = -3.31662479 + -23 x = -3.31662479 + -23 Combine like terms: -3.31662479 + -23 = -26.31662479 x = -26.31662479 Simplifying x = -26.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-19.68337521, -26.31662479}

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